Geometry A - primavera
the following graph shows ABCD and A′B′C′D′ . the following mapping statements describe the transformation of the vertices of the quadrilateral . which function rule correctly describes the transformation from quadrilateral ABCD to quadrilateral A′B′C′D′ ?
(x,y)↦(x+2,y−2)
Which measurements must be known to determine that the triangles are congruent? Select all correct answers.
- BC=3 - AD=4
Ove wants to prove that ABCD is also a rhombus. He uses the properties of parallelograms to show AB≅CD and AD≅CB. What can Ove conclude from this to prove that ABCD is a rhombus?
Ove can conclude that AB≅CD≅AD≅CB due to the Substitution Property of Equality, and thus ABCD is a rhombus.
the rule (x, -y) is a reflection over the y axis .
false
Let K be the midpoint of GI and HJ. Is there enough information to prove quadrilateral GHIJ is a parallelogram? Select the answer that is completely correct.
Yes, since K is a midpoint for the segments, then K bisects GI and HJ. If the diagonals of a quadrilateral bisect each other, then quadrilateral GHIJ is a parallelogram.
which statement is correctly written as a conditional statement ?
if the number 1010 is an even number , then it is a composite number .
use the conditional statement to answer the question . if two rays share a common endpoint, then they form an angle . what is the converse of the given conditional statement ?
if two rays form an angle , then they share a common endpoint .
For △ABC, AC≅AB. Which set of measures is possible for ∠CAB and ∠CBA?
m∠CAB=30∘, m∠CBA=30∘
Did △ABC undergo a dilation to produce the image △A′B′C′?
no
Select the term that best fills in the blank in the following description of a dilation. The dilation of a line segment creates a _[blank]_ line segment, provided the center of dilation is not on the line segment and the scale factor does not equal 1.
parallel
what is the definition of perpendicular lines ?
perpendicular lines are two lines that intersect to form four congruent right angles .
Does the transformation represent a dilation?
yes
which statement is correctly written as a biconditional statement ?
you pass the exam if and only if you score 60% or higher .
Match each numbered statement with the correct reason in the proof.
(.75/1.00) 1. ad is the perpendicular bisector of bc : given 2. ab = ac, db = dc : perpendicular bisector theorem x 3. ab ≅ ac, db ≅ dc : definition of congruent triangles 4. ad ≅ ad : reflexive property of congruence x 5. abd ≅ acd : definition of congruent segments x 6. ∠b ≅ ∠c : sss congruence postulate
use the graph of figure ABCD and its image , figure A′B′C′D′ , to answer the question . the transformation takes each point (x,y) to a new coordinate (x′,y′) . which function correctly describes the transformation ?
(x,y)↦(−x,y)
select two of the following mapping statements that are the result of the same translation .
- (2,−3)↦(5,−8) - (−1,2)↦(2,−3)
A segment is dilated, and the resulting segment is shorter than the original. Which of the following options could be the scale factor of the dilation? Select all that apply.
- 1/5 - 3/8
in triangle abc, cd is a median. the area of △acd =24 cm2 the area of △bcd is equal to _[blank]_ cm2 because _[blank]_.
- 24 - The median connects vertex C to the midpoint of AB.
Which pairs of measures could be the measures of ∠A and ∠C? Select all that apply.
- 55∘,55∘ - 30∘,30∘
Match each numbered statement in the proof to its correct reason.
1. DE is the midsegment of △ABC. : Given 2. DE∥BC : Triangle Midsegment Theorem 3. ∠ADE and ∠ABC are corresponding angles. : Definition of corresponding angles 4. ∠ADE≅∠ABC : Corresponding Angles Postulate
Match each statement in the proof with the correct reason. Notice that the reasons are on the left and the statements are on the right for this problem.
1. Given : ∠HIJ≅∠LKJ HI≅KL 2. Vertical angles are congruent. : ∠HJI≅∠LJK 3. AAS Congruence Theorem : △HIJ≅△LKJ
In right triangle ABC, ∠A is a right angle, m∠B=44∘, and AC=10. What is the measurement of BC?
14.4
Allison drew a map of where she and her friends live. Allison's house is at point A , and her friends live at points B ,C , and D. She only wrote some of the distances, in blocks, on the map. Also, AD is a perpendicular bisector of BC. Allison wants to know the distance between her house and point C.
4.24
if △ABC≅△DEF, what is the length of DF?
4.5
△ABC has a right angle ,∠ABC , and . m∠BCA=45∘. Therefore, m∠CAB= [blank]∘. Enter the number that correctly fills in the blank.
45
Given that DE, DF, and EF are midsegments of △ABC, and DE=3.2 feet, EF=4 feet, and DF=2.4 feet, what is the perimeter of △ABC?
19.2
If △ABC∼△DEF, what is the scale factor for the dilation that maps △ABC to △DEF? Enter your answer as a number.
2
use the figure to complete the sentence. if line e is the perpendicular bisector of bc, and bd = 2, then cd = blank
2
A TV is sized based on the length of its diagonal. The following TV has a length of 17.1 inches and a height of 10.4 inches. What is the TV size (the length of the diagonal)?
20
What is the measure of DC?
20
Use triangle ABC to write the value of tanA as a ratio. What is the ratio for tanA?
24/45
What is the measure of ∠D? Enter the correct value. Do not include the degree symbol.
28
By the SAS Similarity Theorem, △ABC∼△DEF. What is the measure of side ED?
2sqr13
in the following figure, ba ≅ ca, and d is on bc. if bd = 3, then cd = [blank]
3
In right triangle RQS, ∠Q is a right angle, RQ=55, QS=48, and RS=73. What is the ratio of cos S?
48/73
What is the length of segment NQ?
7 units
given: ED is a midsegment of △ABC prove: DE = 1/2 BC match each numbered statement with its correct reason to complete steps 7 to 11 in the proof.
7. ratios of corresponding sides 8. reflexive property 9. sas similarity theorem 10. similar triangles have proportional sides 11. division
What is the value of x?
75
Under a dilation, triangle A(0,0), B(0,3), C(5,0) becomes triangle A′B′C′. The scale factor for this dilation is 3. What is the length of A′B′, in inches?
9
what notation is used to represent the distance from point AA to B ?
AB
Grady wants to prove that △ABC∼△DEF. He notices that ∠ABC≅∠DEF. Which other piece of information can he use to prove the triangles are similar using the Side-Angle-Side Similarity Theorem?
AB/DE=BC/EF
Which answer gives statements that should be used to prove angles 1 and 6 are supplementary angles?
Angles 1 and 2 form a linear pair; angles 2 and 6 are congruent as corresponding angles.
Which answer gives statements that should be used to prove angles 1 and 7 are congruent?
Angles 1 and 3 are congruent as vertical angles; angles 3 and 7 are congruent as corresponding angles.
Which statements should be used to prove angles 1 and 8 are supplementary angles?
Angles 1 and 4 form a linear pair; angles 4 and 8 are congruent as corresponding angles.
Match each statement in the proof to the correct reason.
1. ac ≅ ad, ab is a median of cd : given 2. bc ≅ bd : definition of median 3. ab ≅ ab : reflexive property of congruence 4. △abc ≅△abd : sss congruence postulate
Match each statement in the proof to the correct reason.
1. ac≅ae ab≅ad,∠cab is a rotation of ∠ead : given 2. m∠cab = m∠ead : vertical angles are congruent 3. ∠cab ≅∠ead : definition of congruent angles 4. △abc≅△ade : sas congruence postulate
Tabitha says she can prove that the triangles are congruent by using the SAS Congruence Postulate. Is she correct? Why? _[blank A]_, the triangles have _[blank B]_ labeled with equal measures, so _[blank C]_. Select the three answers that fill in the blanks in the previous sentence to make it a true statement. Select one answer choice for each blank (A, B, and C).
- A: No - B: three pairs of corresponding sides, but no pairs of corresponding angles - it cannot be proven that the triangles are congruent using the SAS Congruence Postulate
If Anna can show that triangles ABD and ACD are congruent, she can find the distance from A to B. Which additional segment lengths could be used to prove that △ADB≅△ADC by using the SAS Congruence Postulate? Select all that apply.
- BD=8 ft. - CD=8 ft.
A right triangle is dilated by a factor of 3.5. Which statements about the resulting triangle must be true? Select all that apply.
- It is larger than the original triangle. - It is a right triangle.
If triangle ABC is reflected onto triangle DEF, then the triangles are congruent https://assets.learnosity.com/organisations/625/asset/media/1157574 Based on this information, what other statement is true?
AB≅DE
If AB=8.2 feet, BD=6 feet, CD=6 feet, and m∠ADC = 90∘, which figure is a perpendicular bisector of △ABC?
AD ( with lines above them )
Which answer gives statements that should be used to prove angles 2 and 8 are congruent?
Angles 2 and 4 are congruent as vertical angles; angles 4 and 8 are congruent as corresponding angles.
Lines m and n are parallel lines cut by a transversal l.
Angles 2 and 6 are congruent as corresponding angles; angles 6 and 7 form a linear pair.
If angles 2 and 8 are alternate interior angles, which angle pair relationships should be used to prove lines mm and n are parallel?
Angles 2 and 8 are congruent as alternate interior angles.
Which angle pair relationships should be used to prove lines m and n are parallel?
Angles 3 and 6 are supplementary same-side interior angles.
Choose the phrase that best fills in the blank to complete the following description of a dilation. A triangle undergoes a dilation with a scale factor of 710. The resulting triangle is _[blank]_ the original triangle.
smaller than
Match the side ratios to the correct trigonometric expression for ∠Z.
tan z = xy/xz cos z = xz/yz sin z = xy/yz
Choose the phrase that best fills in the blank in the following description of a dilation. If point B is the center of dilation for a dilation of line AB, the image of the dilation is _[blank]_.
the same as line AB
use the following information to answer the question . one statement in a proof says , If AB=CDAB=CD and CD=EF ,CD=EF , then AB=EF. AB=EF . what reason can be used for the statement ?
transitive property of equality
describe the transformation that takes place with the following rule : (x - 2, y + 4)
translates 2 units left AND 4 units up .
Which triangle is not congruent to the other three triangles?
triangle D
what is the definition of perpendicular lines ?
two lines that intersect in a way that forms right angles
paola proves that ∠b ≅∠d. she first uses alternate interior angles theorem, then she finds ac ≅ ac by the reflexive property. next, paola uses the asa congruence theorem to show △abc ≅△cda. since corresponding parts of congruent triangles are congruent, ∠b ≅∠d. which pairs of angles could paola have concluded are congruent using the alternate interior angles theorem?
∠1≅∠2 and ∠3≅∠4
use the following figure to answer the question . what is another name for ∠1 ?
∠ABC
What additional measurements must Jordan know to use the AAS Congruence Theorem to prove that the two gussets are congruent?
∠ABC and ∠DEF measure 87∘, and ∠ACB and ∠DFE measure 35∘.
In the figure provided, if ∠B≅ [blank] _, then it is possible to show that △ADE∼△ABC to justify the A Similarity Postulate
∠ADE
Which answer correctly fills in the blank in Statement 2 to complete the proof?
∠C≅∠E
Which answer correctly fills in the blank for Statement 3 of the proof to show that WZ≅XY and XW≅YZ?
∠WXZ≅∠YZX and ∠WZX≅∠YXZ
Which similarity statement is true?
△SRP∼△S′R′P′
It can be proven that △CEF∼△CAB, and since FE is a midsegment, _[blank]_. The corresponding sides in similar triangles must be proportional, so EF=1/2 AB. Which statement best fills in the blank to explain why EF=1/2 AB?
CE=1/2 CA
Which statement correctly explains how to prove △ABC∼△DEF?
Calculate the ratios ABDE, BCEF, and ACDF. If the ratios are the same, the triangles are similar.
a translation can be applied to △abc in a way that ab coincides with de and bc coincides with ef. this causes ∠b to correspond to ∠e. how can you be sure that ac ≅ df?
Endpoints A and C coincide with endpoints D and F.
the distance between two points on a number line can be found by taking the _[blank 1]_ of the _[blank 2]_ of the coordinates . match each blank with the word or phrase that correctly fills in that blank .
blank 1 = absolute value blank 2 = difference
The value of cos87∘ is equivalent to which value?
sin3∘
Which value is equivalent to cos15∘?
sin75∘
Select 3 answers. Select one answer for Question 1, and select two answers for Question 2.
- a rotation is a rigid transformation - △ABC≅△DEF - A rotation can map △ABC onto △DEF.
use the diagram and information to complete the proof. the following table shows steps 1 through 5 of the proof. for steps 6 through 11, match each numbered statement with the correct reason.
6. segment addition postulate 7. substitution property of equality 8. reflexive property of congruence 9. sas similarity theorem 10. corresponding angles of similar triangles are congruent 11. converse of the corresponding angles theorem
What is the measure of ∠A?
60
Grace states that she can use the ASA Congruence Theorem to prove the given triangles are congruent. Is she correct? Why or why not? Select the option that provides the correct answer and the correct reason.
Grace is incorrect because there are no pairs of corresponding angles with the same measures.
Ari wants to prove that LMNO is a square. He begins by using properties of parallelograms and congruent triangles to prove that all sides of LMNO are congruent. He then shows that ∠M≅∠N because they are corresponding parts of congruent triangles. Knowing that consecutive angles in a parallelogram are supplementary allows him to show that m∠M=m∠N=90∘. How can Ari complete the proof? Select all that apply.
- Ari can use the definition of parallelogram to state ∠L≅∠N and ∠M≅∠O. Then he can use the definition of congruence and substitution to show that m∠L=m∠M=m∠N=m∠O=90∘. Thus, parallelogram LMNOLMNO is a square by the definition of a square. - Ari can state that LMNO is a rectangle because it has at least one right angle. Since rectangles have four right angles, he can state that LMNO is a square by the definition of a square.
Which statements describe two similar triangles? Select all that apply.
- two isosceles right triangles - two triangles with two pairs of congruent angles
Which series of transformations shows that polygon ABCDE is congruent to polygon A′B′C′D′E′ by superimposing one onto the other?
a translation 4 units up, followed by a reflection in the y-axis
what term does the statement "the set of all points in a plane that are equidistant from a given point" define ?
circle
what term does the statement "the set of all points in a plane that are the same distance from a given point" define ?
circle
Which value is equivalent to sin42∘?
cos48∘
A triangle has two congruent sides. Which answers list possible types of angles for this triangle? Select two that apply.
- 1 obtuse angle and 2 angles with the same measure of 40∘ - 1 right angle and 2 congruent acute angles
In △ABC, AD≅DB, AE≅EC, DE=4 cm, and DE is a _[blank A]_. Therefore, BC= [blank B]
- A: midsegment - B: 8 cm
Match each numbered statement in the proof with the correct reason.
1. ab ≅ cb, bd bisects ∠abc : given 2. ∠3 ≅∠4 : definition of angle bisector 3. BD≅ BD : reflexive property of congruence 4. abd ≅ cbd : sas congruence postulate 5. ∠1 ≅∠2 : corresponding parts of corresponding triangles are congruent. 6. m∠1 = m∠2 : definition of congruent angles
Match each statement in the proof with the correct reason.
1. abcd is a parallelogram : given 2. ab cd : definition of parallelogram 3. ad is a diagonal of ab and cd : definition of transversal 4. ∠a and ∠d are same-side interior angles : definition of same-side interior angles 5. ∠a is supplementary to ∠d : same-side interior angles theorem
use the figure and the information to complete the proof. given: ABCD is a parallelogram. prove: the diagonals ac and bd bisect each other. match each statement in the proof with the correct reason.
1. abcd is a parallelogram : given x 2. ab ≅ cd, ad ≅ bc : corresponding parts of congruent triangles are congruent 3. 9 ≅ 11 : vertical angles theorem 4. ab cd : definition of parallelogram 5. 2 ≅ 5 : alternative interior angles x 6. aeb ≅ ced : asa congruence theorem x 7. ae ≅ ce and be ≅ de : opposite sides of a parallelogram are congruent 8. e is the midpoint of ac, e is the midpoint of bd : definition of midpoint9. ac and bd bisect each other : definition of bisect
Match each statement in the proof with the correct reason.
1. bc ≅ cd, ac bisects ∠bcd : given 2. ∠1 ≅∠2 : definition of bisect 3. ac ≅ ac : reflexive property of congruence 4. △abc ≅ △adc : sas congruence postulate
Match each statement in the proof with the correct reason.
1. de and df are midsegments of △abc : given 2. de is parallel to bc : triangle midsegment theorem 3. ∠edf and∠dfb are alternative interior angles : definition of alternative interior angles 4. ∠edf ≅∠dfb : alternative interior angles theorem
∠A=8x+2 and ∠B=9x+8 What is the value of x?
10
Nicki is trying to prove that △FEG∼△ABG. She determines that EF∥AB, but she needs to provide a reason. Which reason proves that EF∥AB?
Midsegment Theorem
Is it possible to prove that the triangles are congruent by using the SAS Congruence Postulate?
Yes, there is enough information to use the SAS Congruence Postulate to prove the triangles are congruent.
Segment CD is a median of triangle ABC. Which statement is true about the area of △BCD?
The area of △BCD is equal to the area of △ACD.
A segment is dilated by a factor of 2.52.5 and the resulting segment is parallel to the original segment. Which statement must be true?
The center of dilation is not on the original segment.
A translation can be applied to △ABC in a way that AC coincides with KM and BC coincides with LM. This causes ∠C to correspond to ∠M. How can you be sure that AB≅KL?
The endpoints A and B coincide with the endpoints K and L.
______unit 3 session _________________________________ solve for x ( 2x+15 / x+15 ) Find the value of x (what do you know about consecutive angles of a parallelogram)? ( 9x+15 / 6x+15 ) Find RQ ( -1+4x / 3x+3 ) Find m∠G ( 3x+11 / 5x-9 )
__________________________________________________________________________ x = 0 x = 10 RQ = 15 G = 41
Which single transformation maps figure ABCD to figure A′B′C′D′?
a dilation
hich series of transformations correctly maps trapezoid ABCD to trapezoid A′B′C′D′?
a dilation with a scale factor of 2 about the origin, followed by a reflection in the y-axis
which of the following statements is biconditional ?
a number is an even number if and only if it is divisible by 2 .
Which transformation shows △ABC≅△DEF, by mapping △ABC to △DEF?
a reflection
In triangle ABC, CA=2, CB=2, m∠A=a∘, and m∠B=b∘. Which are the possible values of aa and b?
a=45, b=45
Given: ED is a midsegment of △ABC. Prove: DE∥BC Match each blank with the correct statement or reason that fills in that blank.
blank 1 = definition of midsegment blank 2 = AB=AD+DB , AC=AE+EC blank 3 = SAS similarity theorem blank 4 = ∠AED ≅∠ACB , ∠ADE ≅ ∠ABC
examine the following figure, where de is parallel to AC. the measure of EB is __blank a___ units by the ___blank_b__. thus, BC must measure ___blank c___ units.
blank a = 60 blank b = triangle proportionality theorem blank c = 100
The value of sin35∘ is equivalent to which value?
cos55∘
Which steps are required to prove that the medians of triangle ABC are concurrent? Select all that apply.
- Prove △EDG∼△BCG. - Use the Midsegment Theorem to prove DE = 1/2BC. - Use proportions to show GE = 13 BE and GD = 13 CD. - Draw a line segment from E to D, which is a midsegment. - Draw a median and another midsegment, and repeat the steps to show FG = 13 FA.
Quadrilateral ABCD is dilated, with the center of dilation at the origin (0,0), to result in the image, quadrilateral A′B′C′D′. Which answers are true statements about the transformation that maps quadrilateral ABCD to quadrilateral A′B′C′D′? Select all that apply.
- The transformation doesn't preserve side lengths. - The transformation is a nonrigid transformation. - The transformation preserves angle measures.
Which answers are true statements about the transformation that maps triangle ABC to triangle A′B′C′? Select all that apply.
- The transformation doesn't preserve side lengths. - The transformation is a nonrigid transformation. - The transformation preserves angle measures.
Which answers are true statements about the transformation that maps triangle PRSPRS to triangle P′R′S′? Select all that apply.
- The transformation doesn't preserve side lengths. - The transformation preserves angle measures. - The transformation is a nonrigid transformation.
Which of the following properties can be used to prove quadrilateral WXYZ is a parallelogram? Select all that apply.
- WX≅YZ and WZ≅XY - WX∥YZ and WX≅YZ - WX∥YZ and WZ∥XY
If m∠D=35∘, m∠B=35∘, AD=3 inches, and AB=3 inches, are the two swatches congruent? How do you know? Select two answers: one for the first question and one for the second question.
- Yes, the swatches are congruent. - By the Reflexive Property of Congruence, ∠A≅∠A, so the swatches are congruent by the ASA Congruence Theorem.
Which answer choices give enough information to determine all three angle measures of an isosceles triangle? Select two that apply.
- a triangle with an angle of 90∘ - a triangle with an obtuse angle of 124∘
In the following figure, AC=4 units and CB=4 units. Which statements are true? Select all that apply.
- m∠AED=90∘ - AE=EB
which words or phrases describe parallel lines ? select all that apply .
- never intersect - coplanar lines
Which statements about the triangles are true? Select all that apply.
- △ABC≅△DEF by the SAS Congruence Postulate - A rotation will map △ABC onto △DEF.
Use the diagram and the information to complete the proof. Given: △WXZ and △YXZ are right triangles. WX≅YZ Prove: ∠YZX≅∠WZX Match each statement in the proof with the correct reason.
1. WX≅YZ △WXZ and △YXZ are right triangles. : given 2. XZ≅XZ : reflexive property of congruence 3. △WXZ≅△YXZ : HL congruence theorem 4. ∠YZX≅∠WZX : corresponding parts of congruent angles are congruent
Match each statement in the proof with the correct reason.
1. ab ∥ed bc∥df bc ≅df : given 2. ∠bca ≅∠dfe, ∠bac ≅∠def : alternative interior angles theorem ( got the third one wrong )
Match each statement in the proof with the correct reason.
1. abdc is a quadrilateral. ab∥cd, ∠a ≅∠d : given 2. cb ≅ cb : reflexive property of congruence 3. ∠abc ≅ ∠dcb : alternative interior angles theorem 4. abc ≅ dcb : aas congruence theorem 5. ab ≅ cd : corresponding parts of congruent triangles are congruent 6. abdc is a parallelogram : one pair of opposite sides is both parallel and congruent
Complete the proof by matching each statement with the appropriate reason.
1. given 2. definition of congruent angles 3. aa similarity postulate
Given: △ABC; CD is a median; BE is a median. Prove: △EFD∼△BFC Match each numbered statement in the proof with its correct reason.
1. given 2. definition of midsegment 3. midsegment theorem 4. alternative interior angles theorem 5. aa similarity postulate
Prove △ABC∼△DEF. Match each numbered statement with the correct reason.
1. given 2. definition of right triangle 3. all right angles are congruent 4. the ratio of corresponding sides 5. transitive property of equality 6. sas similarity theorem
match each numbered statement in the proof with the correct reason.
1. given 2. definition of supplementary angles 3. if an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
Given: Triangle ABC has side lengths AB=9, BC=14, and AC=6.5. Triangle DEF has side lengths DE=13.5, EF=21, and DF=9.75. Prove △ABC∼△DEF. Match each numbered statement with the correct reason.
1. given 2. the ratio of corresponding sides 3. transitive property of equality 4. sss similarity theorem
https://assets.learnosity.com/organisations/625/asset/media/1159448 Match each numbered statement with the correct reason.
1. given 2. the ratio of corresponding sides 3. transitive property of equality 4. sss similarity theorem
Complete the proof by matching each statement with the appropriate reason.
1. given 2. triangle angle sum theorem 3. substitution 4. subtraction property of equality 5. definition of congruent angles 6. aa similarity postulate
Match each statement in the proof with the correct reason.
1. j is the midpoint of hl △hij and △lkj are right triangles. ij ≅kj : given 4. △hij ≅△lkj : hl congruence theorem ( got 2 and 3 wrong )
Match each numbered statement in the proof to its correct reason.
1. m∠4 + m∠5 = 180 : given 2. ∠4 and ∠5 are supplementary angles : definition of supplementary angles 3. ∠4 and ∠5 are same-side interior angles : definition of same-side interior angles 4. m∥n : converse of the same-side interior angles theorem
Match each numbered statement in the proof to its correct reason.
1. m∠4=m∠2 m∠5=m∠3 m∠DBE=180∘ : Given 2. m∠4+m∠1+m∠5=m∠DBE : Angle Addition Postulate 3. Because m∠DBE=180∘, m∠4+m∠1+m∠5=180∘. : Transitive Property of Equality 4. Because m∠4=m∠2 and m∠5=m∠3, m∠2+m∠1+m∠3=180∘. : Substitution Property of Equality 5. m∠1+m∠2+m∠3=180∘ : Commutative Property of Addition
Match each numbered statement in the proof to its correct reason.
1. m∥n Line l is a transversal of lines m and n. : Given 2. ∠3 and ∠1 are vertical angles. : Definition of vertical angles 3. ∠3≅∠1 : Vertical Angles Theorem 4. ∠1 and ∠5 are corresponding angles. : Definition of corresponding angles 5. ∠1≅∠5 : Corresponding Angles Postulate 6. ∠3≅∠5 : transitive property of congruence
Match each numbered statement to the correct reason in the proof
1. m∥n : given 2. ∠3 and ∠6 are same-side interior angles : definition of same-side interior angle 3. ∠3 and ∠6 are supplementary : same-side interior angles theorem 4. m∠3 + m∠6 = 180 : definition of supplementary
Match each numbered statement in the proof with the correct reason.
1. m∥n : given 2. m∠1 + m∠5 = m∠abe : angle addition postulate 3. ∠abe and ∠4 are a linear pair : definition of linear pair 4. m∠abe + m∠4 = 180 : linear pair postulate 5. m∠1 + m∠5 + m∠4 = 180 : substitution property of equality 6. ∠2 and ∠4 are alternative interior angles, ∠3 and ∠5 are alternative interior angles : definition of alternative interior angles 7. ∠2 ∠4, ∠3 ∠5 : alternative interior angles theorem 8. m∠2 = m∠4, m∠3 = m∠5 : definition of congruent angles 9. m∠1 + m∠3 + m∠2 = 180 : substitution property of equality 10. m∠1 + m∠2 + m∠3 = 180 : commutative property of addition
Match each numbered statement in the proof to its correct reason.
1. m∥n line l is a transversal of lines m and n : given 2. ∠3 and ∠1 are vertical angles : definition of vertical angles 3. ∠3 ≅∠1 : vertical angles theorem 4. ∠1 and ∠5 are corresponding angles : definition of corresponding angle 5. ∠1 ≅∠5 : corresponding angles postulate 6. ∠3≅∠5 : transitive property of congruence
Match each numbered statement with the correct reason in the proof.
1. ∠3≅∠5 : given 2. ∠3 and ∠5 are alternative interior angles : definition of alternative angles 3. m∥n : converse of the alternate interior angles theorem
Match each statement in the proof with the correct reason.
1. ∠d≅∠b, ad≅ab : given 2. ∠a ≅ ∠a : reflexive property of congruence 3. △ade≅△abc : asa congruence theorem
a segment is on a number line with endpoints at 2.82.8 and 4.6.4.6 . what is the length of the segment ?
1.8
In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5. What is the measurement of EF?
1.97
A woman who is 5 feet tall is standing in the park and notices that her shadow, CB, measures 7 feet. At the same time, she notices that the tree next to her, DE, casts a shadow that measures 14 feet FE How tall is the tree?
10 feet
A tent is set up for an outdoor market. One side of the tent is 9 feet tall. A rope of length p is attached to the top edge of the tent and is secured to the ground. The rope forms a 55∘ angle with the ground. What is the approximate value of p, the length of the rope?
11.0 feet
If m∠SPR=65∘ and m∠PRS=51∘, then m∠PST= [blank]∘.
116
If segment DE is a midsegment of △ABC, then how many meters is segment BC?
12
In right triangle GHI, ∠H is a right angle, m∠I=42∘, and GH=11. What is the measurement of HI?
12.22
Use triangle ABC to write the value of sinB as a ratio. What is the ratio for sinB?
12/13
To find the width of the sinkhole, find the distance between points C and B. What is the distance across the sinkhole?
125m
If △ABC≅△DEF, what is the length of DF?
13
If m∠BCA=45∘, what is the measure of ∠CAD?
135
Becky is standing near a sign post. She is 5 feet, 3 inches tall, and at a certain point in the day she casts a 6-foot shadow. At the same time, the sign post casts an 18-foot shadow. The following figure models this situation. How tall is the sign post?
15 feet, 9 inches
A garden wall is 4 feet in height and has a 6-foot shadow. A tree in the garden casts a 24-foot shadow at the same time of day. What is the height of the tree?
16
Examine the following triangle. https://assets.learnosity.com/organisations/625/asset/media/1159339 Based on the given information, what is the measure of the missing length, w?
16
Examine the following triangle. https://assets.learnosity.com/organisations/625/asset/media/1159361 Based on the given information, what is the measure of the missing length, w?
16
In right triangle ABC, ∠C is a right angle, m∠A=52∘, AC=10, and AB=c. What is the measurement of AB?
16.23
If DE∥AC, what is the measure of length a?
21
examine parallelogram abcd. sides cd and ab have lengths of y + 18 and 4y, respectively. determine the value of y and answer the following question. what is the length of ab?
24
In right triangle XYZ, ∠Z is a right angle, m∠Y=16∘, and XZ=7. What is the measurement of YZ?
24.4
Match each numbered statement for steps 3 through 7 with the correct reason.
3. alternative interior angles theorem 4. reflexive property of congruence 5. aas congruence theorem 6. corresponding parts of congruent triangles are congruent 7. if one pair of opposite sides are both parallel and congruent, then the quadrilateral is a parallelogram.
What is the measure of side FD?
3.4 units
A dilation by a factor of 78 maps triangle ABC to triangle XYZ. Segment BC has a length of 4 cm. What is the length of segment YZ?
3.5cm
If BD=3.7 units and AC=4.1 units, what is the length of BC?
3.7
In right triangle ABC, ∠A is a right angle and sin C=35. What is the ratio for tan C?
3/4
A rope is used to tie a boat to a dock. The angle of depression from the boat to the ocean floor directly beneath the dock is 40∘. The boat is 25.17 feet above the ocean floor. What is the length of the rope between the boat and the dock?
30
A TV is sized based on the length of its diagonal. The following TV has a size (diagonal) of 36 inches and a height of 14.94 inches. What is the TV's length?
32.75 inches
If △ABC≅△FDE, what is the measure of ∠ACB?
34.7∘
What is the measure of ∠R?
36.9
Match each numbered statement for steps 4 through 9 with the correct reason.
4. LN≅LN : reflexive property of congruence 5. △LNO≅△NLM : AAS congruence theorem 6. ∠3≅∠4 : corresponding parts of congruent triangles are congruent 7. ∠L=∠1+∠3 ∠N=∠2+∠4 : angle addition postulate 8. ∠L=∠2+∠4 ∠N=∠2+∠4 ∠L≅∠N : substitution property of equality 9. LMNO is a parallelogram : if both pairs of opposite angles of a quadrilateral is a parallelogram
Match each numbered statement for steps 4 through 8 with the correct reason.
4. vertical angles theorem 5. asa congruence theorem 6. corresponding parts of congruent triangles are congruent 7. definition of bisect 8. if diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
a protractor is used on an angle. One ray of the angle is at 46∘46∘ and the other ray is at 95∘.95∘ . what is the measure of the angle ?
49∘
Segments CE and BE have lengths 15−x and 2x, respectively What is the value of x?
5
Given: △ABC∼△CBD AC2=AB⋅AD Prove: CB2+AC2=AB2 Match each statement in the following steps of the proof with the correct reason.
5. factor 6. segment addition postulate 7. substitution 8. multiply
A 6-foot-tall man is standing in front of a school and notices his shadow measures 10 feet. At the same time, he notices a nearby flagpole casts a shadow that measures 85 feet. How tall is the flagpole?
51 feet
A Ferris wheel is 136 feet tall. It casts a 34-foot shadow. What is the height, in feet, of a nearby man that casts a shadow of 1.5 feet?
6
Given: DE∥AC Prove: BD/DA=BE/EC For steps 6 through 11, match each numbered statement with the correct reason.
6. segment addition postulate 7. substitution property of equality 8. expansion of fractions 9. divide 10. subtraction property of equality 11. reciprocals of both sides
use the diagram and information to complete the proof. the following table shows steps 1 through 5 of the proof. for steps 6 through 11, match each numbered statement with the correct reason.
6. segment addition postulate 7. substitution property of equality 8. expansion of fractions 9. division 10. subtraction property of equality 11. reciprocals of both sides
In right triangle JKL, ∠L is a right angle, m∠J=62∘, and JK=17. What is the measurement of JL?
8
Given: BD/DA=BE/EC Prove: DE∥AC For steps 6 through 11, match each numbered statement with the correct reason.
6. segment addition postulate 7. substitution property of equality 8. reflexive property of congruence 9. sas similarity theorem 10. corresponding angles of similar triangles are congruent. 11. converse of the corresponding angles theorem
Use the figure and information to complete steps 6 through 10 in the proof. Match each numbered statement in the proof with the correct reason.
6. ∠2 and ∠4 are alternative interior angles, ∠3 and ∠5 are alternative interior angles : definition of alternative interior angles 7. ∠2 ∠4, ∠3 ∠5 : alternative interior angles theorem 8. m∠2 = m∠4, m∠3 = m∠5 : definition of congruent angles 9. m∠1 + m∠3 + m∠2 = 180 : substitution property of equality 10. m∠1 + m∠2 + m∠3 = 180 : commutative property of addition
use the diagram and information to complete the proof. the following table shows steps 1 through 6 of the proof. for steps 7 through 11, match each numbered statement with the correct reason.
7. substitution property of equality 8. expansion of fractions 9. division 10. subtraction property of equality 11. reciprocals of both sides
use the diagram and information to complete the proof. the following table shows steps 1 through 5 of the proof. for steps 7 through 11, match each numbered statement with the correct reason.
7. substitution property of equality 8. reflexive property of congruence 9. sas similarity theorem 10. corresponding angles of similar triangles are congruent 11. converse of the corresponding angles theorem
a segment is on a number line with endpoints at −13.6−13.6 and −6.2.−6.2 . what is the length of the segment ?
7.4
In right triangle ABC, ∠B is a right angle and AB=72, BC=65, and AC=97. What is the ratio of sin C?
72/95
Matt wants to measure the height of a tree. He walks exactly 100 feet away from the base of the tree and looks up at it. The angle from his eyes to the top of the tree is 35∘. If his eye level is 5 feet from the ground, what is the height of the tree?
75.02
Choose the value that best fills in the blank in the following description of a dilation. A graphic is printed on a circular banner that has a diameter of 4 feet. The same graphic undergoes a dilation with a scale factor of 1/6 to be printed on circular stickers. The diameter of the dilated graphic is _[blank]_ inches.
8
Determine the value that fills in the blank to make the statement true. Under a dilation with a scale factor of 45, a 10-inch segment becomes a _[blank]_-inch segment. Enter your answer as a number.
8
You can prove that quadrilateral ABCD is a parallelogram by showing that AD∥BC, because if one pair of opposite sides are both parallel and congruent, the quadrilateral is a parallelogram. Which plan should you use to prove AD∥BC?
Angles CAD and ACB are alternate interior angles, and they are congruent. So, AD∥BC by the Converse of the Alternate Interior Angles Theorem.
If AB=3 cm, AC=5 cm, CD=3 cm, and CE=5 cm, what additional information is needed to prove △ABC≅△DEF?
BC=4 cm and DE=4 cm
Joe knows that AD and BC are perpendicular roads. If he can prove △ABD≅△ACD, he can be sure that the two stores are the same distance from his house. Which roads or sections of roads should Joe measure to use the SAS Congruence Postulate to prove △ABD≅△ACD?
BD and CD ( with lines above )
Triangle ABC has side lengths AB=16, BC=13, and AC=7. Triangle DEF has side lengths DE=4, EF=3.25, and DF=1.75. Janna needs to prove △ABC∼△DEF. Which methods can she use to help her prove the triangles are similar by the SSS Similarity Theorem? Select all that apply.
DE/AB=EF/BC=DF/AC=14 x DE/AB=EF/BC=AC/DF=14 ( .25/1)
Triangle ABC is reflected over the y-axis. Which additional transformation proves that △ABC∼△DEF?
Dilate about the origin with a scale factor of 3 to get △DEF.
If AB¯≅CB¯ is given, how can it be proved that m∠A=m∠C?
Draw a segment from B to a point D such that D is the midpoint of AC. Then, show that corresponding sides of new triangles ABD and CBD are congruent. Finally, use the Side-Side-Side Congruence Postulate and the definition of congruent angles to show m∠A=m∠C.
If it is given that AB≅CB, how can it be proved that m∠A=m∠C?
Draw an angle bisector from B to a point D such that D is on AC. Then, show that corresponding sides and the angle between these sides of new triangles ABD and CBD are congruent. Finally, use the Side-Angle-Side Congruence Postulate and the definition of congruent angles to show m∠A=m∠C.
Lina wants to place a triangular design element into a table she is building. What additional information is needed for Lina to use the HL Congruence Theorem to prove that △GHJ≅△IHJ?
GJ≅IJ
* i accidentally refreshed the page of the session quiz for unit 2 so i don't have the questions but i have the answers for them 😭😭
Hl , SSS , SAS , AAS , ASA ---------------------------- SSS ---------------------------- AEB = CED ---------------------------- not enough information
Which statement best explains why EF∥AB?
It can be proven that △CEF∼△CAB, which means that their corresponding angles are congruent. When two lines are cut by a transversal to form congruent corresponding angles, the lines must be parallel.
rectangle PQRS is shown below . points J , K, M, and N are the midpoints of their respective sides . a reflection over which of the following line segments will carry rectangle PQRS onto itself ? select all that apply .
JK , MN ( with lines above them )
An architect constructs a small model of a frame of a house using wooden sticks. The incomplete face of the model roof is shown below, where two parts, PR and ST, are connected. The architect wants to connect P to S and P to T by using two other different wooden sticks.
Join PR and ST so that they form a right angle with a vertex at the midpoint of ST.
She wants to connect the sticks so that the edges of the paper have certain measurements. She wants KM=KN and ML=NL. How should she position the sticks?
Place KL at a right angle on MN so it bisects MN.
Which sequence of transformations maps the points of △GHI onto △G′H′I′, showing that △GHI is similar to △G′H′I′?
Rotate △GHI 90∘ clockwise about the origin and dilate it by a factor of 23 through the origin.
Which answer correctly describes how to complete the proof?
Show that ∠D and ∠E are supplementary by definition. Then, since ∠D is supplementary to both of its consecutive angles, quadrilateral DEGF is a parallelogram.
The Pythagorean Theorem can be proved using similar triangles and proportions. How can you show that △ACD and △CBD are similar to △ABC?
Show ∠ACB≅∠ADC≅∠CDB because they are all right angles. Then ∠A≅∠A and ∠B≅∠B by the Reflexive Property of Congruence. This means △ABC∼△ACD and △ABC∼△CBD by the AA Similarity Postulate.
Klaus's house is located at point K, and his friend Genny's house is located at point G. The public library and science museum, which they often visit together, are located at point L and M, respectively. Klaus and Genny think that the library is the same distance from both of their houses and that the museum is the same distance from both of their houses. Which statement proves their assumptions?
The street with the library and museum crosses the street with the houses at a 90∘ angle and is equidistant from both houses.
A dilation maps triangle PRS to triangle P′R′S′. Which statement is true about the transformation?
The transformation is nonrigid and results in similar triangles.
Which statement best explains whether △ABC is similar to △DEF?
The triangles are not similar because 613≠820.
Which statement best describes the relationship between the triangles?
The triangles are not similar because they do not have
Which statement best explains whether △ABC is similar to △DEF?
The triangles are similar because DF/AC=EF/BC, and ∠C≅∠F.
Which statement best describes the relationship between the triangles?
The triangles are similar because they have 3 pairs of congruent angles.
Which statement best explains whether △ABC is similar to △DEF?
There is not enough information to determine whether the triangles are similar.
A dilation maps figure ABCD to figure A′B′C′D′. Which statement best interprets the relationship between the two figures?
They are similar because dilations are similarity transformations.
Given that AD is a perpendicular bisector of BC, what steps will prove that A is equidistant from B and C?
Use the given information to show that AD intersects BC at right angles, and then prove triangles ABD and ACD congruent using the ASA Congruence Postulate . Next, show congruent sides using the definition of congruent triangles. Finally, use the definition of congruent sides to show AB=AC.
You can prove that KLMN is a parallelogram by showing that its diagonals bisect each other. Which plan should you use to prove that the diagonals bisect each other?
Use ∠1≅∠2, ∠3≅∠4, and XV≅ZV to show △WVZ≅△YVX by the AAS Congruence Theorem. Then, use WV≅YV and XV≅ZV to prove WY and XZ bisect each other.
In right triangle ABC, ∠A is a right angle and sinC=15/17.
What is the ratio cosC?
_____ Unit 4 Session _______________________________________________________________________ The two triangles below are similar. Find the remaining side What is the measure of angle B if the two triangles are similar? What are similar triangles? Find the value of x, if each pair of triangles is similar?
_______________________________________________________________________________ ? = 12 B = 45 Two triangles that have all congruent angles and all the sides are proportional. x = 50
_________Unit_6_Exam_(_Cont_._)__________________________________________________________ Use △ABC, in which AB=48, AC=64, and BC=80, to answer the question. What is the ratio for cosB? Use △ABC, in which AB=37, AC=35, and BC=12, to answer the question. What is the ratio for tanB? Which value is equivalent to sin20∘? Which value is equivalent to cos10∘? In right triangle PQR, ∠P is a right angle, m∠R=58∘, and QR=15. What is the measurement of PQ?
_______________________________________________________________________________ 3/5 ( got it wrong but it's ) 35/12 cos70∘ sin80∘ 12.72
_________________Unit 5 session_____________________________________________________________ what is the ratio for sin A ? what is the ratio for cos A? what is the ratio for tan A? angle for A
_______________________________________________________________________________ 3/5 4/5 3/4 36.? ( i forgot the last number )
_________Unit_6_Exam_(_Cont_._)__________________________________________________________ In right triangle ABC, ∠C is a right angle, m∠B=70∘, and AB=13 What is the measurement of BC? In right triangle RST, ∠T is a right angle, m∠S=41∘, and ST=8. What is the measurement of RT? What is the measure of ∠E? Andrew wants to measure the height of a traffic light. He walks exactly 20 feet from the base of the traffic light and looks up at it. The angle from his eyes to the top of the traffic light is 40∘. Andrew's eyes are at a height of 5 feet when he looks up. How tall is the traffic light? The traffic light is approximately _[blank]_ feet tall. Meg is walking around her neighborhood. She stands 150 meters from the grocery store, and she wants to know the distance between the store and the bank Which answer is closest to the distance between the store and the bank?
_______________________________________________________________________________ 4.4 6.95 45 21.78 162.5 meters
_________Unit_6_Exam__________________________________________________(_93.33/100_)_ Use the figure and information to complete steps 5 through 8 in the proof. Based on the given information, what is the measure of the missing length, c? Violeta wants to install new tiling in her kitchen. She places two triangular tiles together as shown in the following figure. In order to plan her installation, she needs to find the length of BC. The length of BC is _[blank]_ units. Melody lives 30 miles due south of her cousin's house and 40 miles due west of her grandparents' house. One day, she drove to her cousin's house in a straight line from her grandparents' house. How far did she drive? Melody drove _[blank]_ miles. Use △XYZ, in which ∠X is a right angle and tanY=8/15 What is the ratio for sinY?
_______________________________________________________________________________ 5 . factor 6 . segment addition theorem 7 . substitution 8 . multiplication 5 25 50 8/17
_________Unit session 6_____________________________________________________________________ Find the sin of angle T. Find the cos of angle T. Find the tan of angle T. Solve for the missing side of the triangle.
_______________________________________________________________________________ 7/25 24/25 7/24 11.98
Which series of transformations correctly maps triangle ABC to triangle A′B′C′?
a reflection in the y-axis, followed by a translation 3 units down
Which transformation will show that △ABD≅△ABC?
a reflection over AB
When using the Triangle Proportionality Theorem to solve for BE, you need to set up the proportion _[blank 1]_, which yields the correct measure of _[blank 2]_ for length BE.
blank 2 = 28 blank 1 = 46/23 = BE/14
in the following graph , trapezoid ABCD is transformed by a reflection in the y-axis followed by a rotation 180∘ clockwise about the origin to obtain trapezoid A′B′C′D′ . which answer correctly shows the image, trapezoid A′B′C′D′?
https://assets.learnosity.com/organisations/625/asset/media/1158169 or https://cdstools.flipswitch.com/asset/media/1158169
use the conditional statement to answer the question . if a polygon has three sides , then it is a triangle . what is the converse of the given conditional statement ?
if a polygon is a triangle , then it has three sides .
which statement is correctly written as a conditional statement ?
if four is a perfect square , then you can evaluate its square root .
Choose the phrase that best fills in the blank for the following description of a dilation. A triangle undergoes a dilation with a scale factor of 95. The resulting triangle is _[blank]_ the original triangle.
larger than
which term correctly describes the object labeled b in the figure ?
line
use the image to help you complete this problem . match each figure with the correct term .
line = ac plane = p point = b
what term does the description "two lines that intersect to form four congruent right angles" define ?
perpendicular lines
wse the figure to answer the question . what is the correct name for the angle formed by adding ∠1∠1 and ∠2 ?
∠ABD
what is another name for ∠2 ?
∠CBD
the following transformation maps △ABC to △A′B′C′ . which answer correctly describes the transformation applied to △ABC ?
△ABC is moved 44 units left and 11 unit up to create △A′B′C′.
an angle is measured with a protractor . one ray of the angle is at 37∘37∘ and the other ray is at 112∘.112∘ . what is the measure of the angle ?
75∘
use the figure to answer the question .
AB ( with a line above )
use the following statement to answer the question . if AB=CD , then AB+6=CD+6 if the statement is used in a two-column proof , what is the correct reason for the statement ?
Addition Property of Equality
if the point of the preimage is (5,2) and the point of the image is (1,2), what RULE was applied to the preimage to obtain the image ?
(x - 4, y)
use the graph to answer the question . Triangle ABC is reflected over line ll to result in the image, triangle A′B′C′ . which statements are true about the transformation that maps triangle ABC to triangle A′B′C′ ? select all that apply .
- the angle measures remain the same from the preimage to the image . - the transformation is a rigid transformation . - the side lengths remain the same from the preimage to the image .
what must be true in order for two lines to be parallel ? there is more than one correct answer . select all that apply .
- the lines must never intersect . - the lines must be in the same plane .
use the graph to answer the question . which statements are true about the transformation that maps triangle ABC to triangle A′B′C′ ? select all that apply .
- the transformation is a rigid transformation . - triangle A′B′C′ is the result of a reflection . - the transformation preserves side lengths and angle measures .
Match each statement in the proof with the correct reason.
1. ac≅ad , ab bisects cd : given 2. bc ≅ bd : definition of bisect 3. ab ≅ ab : reflexive property of congruence 4. △abc ≅ △abd : sss congruence postulate
the distance between point AA and point BB is _[blank]_ units . enter your answer as the number that correctly fills in the blank in the previous sentence .
3
which of the following transformations map polygon ABCD to itself ? select all that apply .
- a 180∘ clockwise rotation about the origin - a reflection in the x-axis - a 90∘ clockwise rotation about the origin - a reflection in the line y=x - a reflection in the y-axis
use the following graph to answer the question . which answer choices correctly describe the rotation that maps figure ABCD to figure A′B′C′D′ ? select two that apply .
- a 270∘ clockwise rotation about the origin - a 90∘ counterclockwise rotation about the origin
Which series of transformations shows that parallelogram ABCD is congruent to parallelogram A′B′C′D′ by superimposing one onto the other?
a rotation 90∘ clockwise about the origin, followed by a translation 3 units down
apply the rule (-x, y - 2) to the following point, what is the result ? (-3, 5)
(3, 3)
Points G through L bisect the sides of the figure. Point _[blank A]_ is the center of symmetry, and the angle of rotational symmetry is _[blank B]_. Select two answer choices: one for blank A and one for blank B.
- blank A: O - blank B: 60∘
Match each statement in the proof with the correct reason
1. ac ≅ ad, ab bisects cd : given 2. bc ≅ bd : definition of bisect 3. ab ≅ ab : reflexive property of congruence 4. abc ≅ abd : sss congruence postulate
a segment is on a number line with endpoints at −5.3−5.3 and 8.7.8.7 . what is the length of the segment ?
14
a protractor is used on an angle . one ray of the angle is at 13∘13∘ and the other ray is at 57∘.57∘ . what is the measure of the angle ?
44∘
If △ABC≅△KLM, then m∠B= [blank]∘. Enter the value that correctly fills in the blank in the previous sentence. Do not include the degree symbol.
48
A series of rigid transformations are applied to △ABC such that side AB coincides with side DE, side BC coincides with side EF, and side CA coincides with side FD. What is true about angle A?
Angle A coincides with angle D, because the respective sides that form each of the angles coincide.
What is true about angle C?
Angle C coincides with angle F, because the respective sides that form each of the angles coincide.
which series of transformations correctly maps parallelogram ABCD to parallelogram A′B′C′D′ ?
a rotation 90∘ clockwise about the origin , followed by a translation 33 units down
Triangle ABC is translated 1 unit right and 3 units down, and then reflected in the x-axis to produce an image, triangle DEF. Is △ABC≅△DEF?
Yes, the triangles are congruent to each other.
Use the diagram to answer the question. https://assets.learnosity.com/organisations/625/asset/media/1157555 Which transformation maps polygon ABCD to itself?
a reflection in the y-axis
which series of transformations correctly maps rectangle ABCD to rectangle A′B′C′D′ ?
a reflection in the y-axis, followed by a translation 1 unit down
draw a line segment with endpoints M and R . Now draw a parallel line segment that is the same length as MR with the endpoints M′ and R′ in the same order. which answer correctly describes the transformation from MR to M′R′?
a translation
which answer correctly describes the transformation from the preimage to the image ?
a translation 10 units left and 8 units down
let p be the statement "I do my chores," and let q be the statement "I get my allowance." which statement uses pp as the hypotheses and q as the conclusion ?
if I do my chores , then I get my allowance .
Which statement about △ABC and △DFE is true?
△ABC≅△DFE by the SSS Congruence Postulate.
use the image to answer the question . which answer choice correctly names the circle ?
⨀A
what is the correct name of the circle ?
⨀S
Which of the two triangles are congruent? Be sure to select two answers.
- △ABC - △DEF
use the following information to answer the question . what is the reason for Statement 3 ?
Addition Property of Equality
use the following image to answer the question . what statement can be used to prove that vertical angles ∠1 and ∠3 are congruent ?
m∠1+m∠2=m∠2+m∠3
A window is made of two triangular panels of glass, as shown. It is given that WX≅WY and WZ bisects XY Four students explain how they can prove the two triangular panels, △XWZ and ,△YWZ, are congruent. Which student is correct?
Trisha says that it is given that WX≅WY. Since WZ bisects XZ≅YZ , and WZ is congruent to itself. Then, by the SSS Congruence Postulate △XWZ≅△YWZ.
the following mapping statements describe the transformation of the vertices of △ABC to the vertices of its image , △A′B′C′ . what is the correct description of the transformation that maps triangle ABC to triangle A′B′C′ ?
a reflection in the y-axis
Which series of transformations can be used to show that the lower triangle is an image of the upper triangle?
a rotation of 180∘ around point J, then a translation to the left
draw a line . now draw a line perpendicular to the first line that passes through point G (which is not at the intersection) . Measure the distance of G from the first line . draw another point on the second line that is the same distance as G , but is on the opposite side of the first line . if G is the preimage, and the second point is the image , what transformation does this show ?
reflection
which answer gives all of the lines of symmetry that carry the regular polygon onto itself ?
reflections across lines a , b , c , d , e , f and g
Which answers need to be true to be able to use the SSS Congruence Postulate to prove △ABC≅△DEF? Select all that apply.
- AC≅DF - AB≅DE - BC≅EF ( they all have lines above )
Triangle ABC is translated 1 unit right and 3 units down to produce its image, triangle DEF. Which statements are true? Select all that apply.
- △ABC≅△DEF - ∠B≅∠E - AC≅DF
use the following figure to help you complete the sentence . the distance between point AA and point BB is _[blank]_ units .
5
Tony needs to prove that the following two triangles are congruent using rigid transformations. https://assets.learnosity.com/organisations/625/asset/media/1157575 Which set of transformations could Tony use to show that Figure 2 is an image of Figure 1?
a reflection, then a rotation around point L
what term does the statement "a figure formed by two rays that share a common point" define ?
angle
the coordinates of the vertices of trapezoid ABCD are A(−1,4) , B(0,2) , C(1,2) and D(2,4) . ABCD is first rotated 90∘ counterclockwise , and then translated 3 units right. which graph shows the final image A′B′C′D′ ?
https://assets.learnosity.com/organisations/625/asset/media/1157542 or https://cdstools.flipswitch.com/asset/media/1157542
two coplanar lines that never intersect are called parallel lines . what information , if any , should be changed in the previous sentence to correctly define parallel lines ?
the sentence does not need to be changed .
what does the statement "a logical argument written with statements in one column and the corresponding reason in another column" define ?
two-column proof
use the following image to answer the question . which statement can be used to prove ∠2≅∠4 ?
∠1 is supplementary to both ∠2 and ∠4 .
in the following graph , triangle ABC has been transformed in three different ways, resulting in triangle DEF , triangle GHI , and triangle JKL match each triangle with the single transformation that maps △ABC to that triangle .
△def : rotation △ghi : translation △jkl : reflection
use the figure to answer the question . what is the correct way to name the circle ?
⨀B
use the number line to complete the sentence . the distance from point AA to point BB is _[blank]_ units .
5
what is the angle of rotational symmetry for the figure ?
51.4∘
what term does the statement "the set of all points on a circle between two given points on the circle" define ?
arc
Use the following regular polygon to answer the question. https://assets.learnosity.com/organisations/625/asset/media/1157556 Points H through N bisect the sides of the figure. Which of the following transformations map the figure onto itself? Select all that apply.
- a reflection over line CM - a rotation of about 205.6∘ about its center - a reflection over line EH - a rotation of about 51.4∘ about its center
use the diagram and information to complete the proof . match each reason in the proof with the correct statement .
1. ∠1 and ∠2 are supplementary angles. ∠2 and ∠3 are supplementary angles : given 2. m∠1+m∠2=180∘ m∠2+m∠3=180∘ : definition of supplementary angles 3. m∠1+m∠2=m∠2+m∠3 : substitution property of equality 4. m∠1=m∠3 : subtraction property of equality 5. ∠1≅∠3 : if two angles have the same measure , then they are congruent
use the given information to complete the proof . match the reason with the provided statements to complete the proof .
1. ∠A and ∠B are supplementary angles. ∠B and ∠C are supplementary angles : given 2. m∠1+mB∠2=180∘ m∠B+m∠C=180∘ : definition of supplementary angles 3. m∠A+m∠B=m∠B+m∠C : substitution property of equality 4. m∠A=m∠C : subtraction property of equality 5. ∠A≅∠C : if two angles have the same measure , then they are congruent
the distance between point XX and point YY is _[blank]_ units . enter your answer as the number that correctly fills in the blank in the previous sentence .
6
use the conditional statement to answer the question . if a rectangle is a square , then it has four congruent sides . what is the converse of the given conditional statement ?
if a rectangle has four congruent sides , then it is a square .
which statement is correctly written as a conditional statement ?
if a shape has four sides , then it is a quadrilateral .
use the definition of a parallelogram to complete the biconditional statement . a parallelogram is a quadrilateral with two pairs of parallel sides . a quadrilateral is a parallelogram _[blank]_ . which answer correctly fills in the blank in the previous sentence ?
if and only if it has two pairs of parallel sides
which term correctly describes the object labeled a in the figure ?
point
match each type of transformation with the correct description of that transformation .
rotation : the distance between the center of rotation and a point in the preimage is the same as the distance between the center of rotation and the corresponding point on the image . translation : every point in the preimage is mapped the same distance and direction to the image . reflection : every point in the preimage is mapped the same distance from the line of reflection to the image .
