Math Cumulative Exam

Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is the distance from Tia's home to Lei's home. Where is the fruit market? 6th Street and 11th Avenue 10th Street and 17th Avenue 9th Street and 15th Avenue 8th Street and 14th Avenue

b

What is the measure of JHN? 25° 45° 50° 95°

b

Which represents an exterior angle of triangle EGF? ∠MEG ∠NEG ∠PEQ ∠RFS

b

Which rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C'? (x, y) → (x + 7, y + 6) (x, y) → (x + 7, y - 6) (x, y) → (x - 6, y + 7) (x, y) → (x + 6, y + 7)

b

Which shows the pre-image of triangle X'Y'Z' before the figure was rotated 90° about the origin?

b

Which figures are shown in the diagram? Select three options. line CD point D ray CD ray DC segment CD

b,c,e

Quadrilateral ABCD is translated up and to the right, and then rotated about point Q. Which congruency statement is correct? ABCD ≅ WXYZ ABCD ≅ ZYXW ABCD ≅ WZYX ABCD ≅ ZWXY

b

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

b

A right angle intersects a line at point M. Which statement is true about angles 1 and 2? They are congruent. They are right angles. They are complementary. They are supplementary.

c

Are the triangles congruent? Why or why not? Yes, A ≅ D and AB ≅ DE. Yes, they are congruent by either AAS or ASA. No, C is not congruent to any angle in DEF. No, the congruent sides do not correspond.

c

Consider the diagram. What is QS? 2 units. 5 units. 17 units. 33 units.

c

If a translation T-3,-8(x,y) of is applied to square ABCD, what is the y-coordinate of B'? -12 -8 -6 -2

c

A line segment has endpoints at (3, 2) and (2, -3). Which reflection will produce an image with endpoints at (3, -2) and (2, 3)? a reflection of the line segment across the x-axis a reflection of the line segment across the y-axis a reflection of the line segment across the line y = x a reflection of the line segment across the line y = -x

a

Angle KLM and angle MLN are a linear pair. Ray LR is to be added to the diagram so that it is opposite ray LM. Which is true about angle RLN that would be formed? Angles RLN and MLK would be vertical angles. Angles RLN and MLN would be vertical angles. Angles RLN and KLM would be a linear pair. Angles RLN and KLN would be a linear pair.

a

Complete the paragraph proof. Given: M is the midpoint of Prove: ΔPKB is isosceles It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because _____________. Finally, ΔPKB is isosceles because it has two congruent sides. corresponding parts of congruent triangles are congruent base angles of isosceles triangles are congruent of the definition of congruent segments of the definition of a right triangle

a

If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS

a

In the diagram, the ratios of two pairs of corresponding sides are equal. To prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that ∠N ≅ ∠Z ∠N ≅ ∠X ∠L ≅ ∠Z ∠L ≅ ∠Y

a

Point E is drawn on the graph so that line EF is parallel to line CD. If the coordinates of point E are (, y), what is the value of y? −8 −4 0 8

a

Rectangle ABCD was dilated to create rectangle A'B'C'D. What is AB? 6 units 7.6 units 9.5 units 12 units

a

Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1. Which diagram illustrates these transformations?

a

Triangle DEF is an isosceles, so DEF DFE. Angle DEF measures 75°. What is the measure of angle CFD? 105° 125° 150° 165°

a

What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the line y = x? (10, -2) (-10, 2) (-2, -10) (2, 10)

a

Which best explains why the orthocenter of an obtuse triangle is outside the triangle? All three of the altitudes lie entirely outside the triangle. Two of the altitudes lie entirely outside the triangle. All three of the medians lie entirely outside the triangle. Two of the medians lie entirely outside the triangle.

a

Which is precisely defined using the undefined terms point and plane? circle line segment perpendicular lines ray

a

Which statements regarding EFG are true? Select three options. EF+FC>EG EG+FG>EF EG-FG<EF EF-FG>EG EG+EF<FG

a,b,c

Myra took a picture of the sky one afternoon when two jet airplanes appeared to draw a pair of parallel lines with their vapor trails. The vapor trails from two other jets flying from another direction crossed over the parallel trails. She printed her picture and labeled the angles and lines. Assume lines c and d are parallel and 2 measures 98°. Which statements are true? Select three options. m3 = m6 = 98° m3 = m14 = 98° m4 = m8 = 82° m4 = m12 = 82° m5 = m8 = 82°

a,c,e

Which statements about the diagram are true? Select three options. x = 63 y = 47 z = 117 x + y = 180 x + z = 180

a,c,e,

An isosceles right triangle has leg lengths of 4 centimeters. What is the length of the altitude drawn from the right angle to the hypotenuse? 2 cm 2 squareroot 2 cm 4 cm 4 squareroot 2 cm

b

Consider the triangle. Which statement is true about the lengths of the sides? Each side has a different length. Two sides have the same length, which is less than the length of the third side. The three sides have the same length. The sum of the lengths of two sides is equal to the length of the third side.

b

Figure RHOM is a rhombus. and are the diagonals of the rhombus, as well as angle bisectors of the vertex angles, and they create four isosceles triangles: HOM, MHR, RHO, and OMR. What is true about MSR? It must be acute. It must be a right angle. It must be equal to MRH. It must be equal to RMS

b

For the triangles to be similar by the SSS similarity theorem, what must be the value of y? 18 20 24 26

b

Given that D is the midpoint of AB and B is the midpoint of AC, which statement must be true? AD = AC AC = 4DB AB + DC = AC BK = KC

b

Given: a ∥ b and ∠1 ≅ ∠3 Prove: e ∥ f We know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem. Which information is missing in the paragraph proof? ∠2 ≅ ∠4 ∠1 ≅ ∠2 ∠2 ≅ ∠3 ∠1 ≅ ∠4

b

Is there a series of rigid transformations that could map KLP to QNM? If so, which transformations? No, KLP and QNM are congruent but KLP cannot be mapped to QNM using a series rigid transformations. No, KLP and QNM are not congruent. Yes, KLP can be reflected across the line containing KP and then translated so that P is mapped to M. Yes, KLP can be rotated about P and then translated so that L is mapped to N.

c

Line ST and point V are shown on the graph. Line VW is to be drawn on the graph such that it is perpendicular to line ST. If the coordinates of point W are (−1, y), what is the value of y? −7 −5 2 3

c

Point O is the incenter of ΔABC. What is QBO? 5° 9° 12° 24°

c

Point S lies between points R and T on . If RT is 10 centimeters long, what is ST? 2 centimeters 4 centimeters 6 centimeters 8 centimeters

c

Triangle RST has vertices R(2, 0), S(4, 0), and T(1, -3). The image of triangle RST after a rotation has verticesR'(0, -2), S'(0, -4), and T'(-3, -1). Which rule describes the transformation? R0, 90° R0, 180° R0, 270° R0, 360°

c

Two parallel lines are crossed by a transversal. If m1=61.8°, then what is the measure of m6? 61.8° 81.8° 118.2° 128.2°

c

What is the length of ? 1.89 ft 2.43 ft 3 ft 7 ft

c

What is the length of line segment LJ? 9 units 12 units 15 units 18 units

c

Which piece of additional information can be used to prove that △RST ~ △VUT? RT = ST 3ST = UT ∠R ≅ ∠V ∠V ≅ ∠U

c

Which set of equations is enough information to prove that lines c and d are parallel lines cut by transversal p? m∠1 = 81° and m∠2 = 99° m∠3 = 99° and m∠4 = 99° m∠2 = 99° and m∠4 = 99° m∠4 = 81° and m∠1 = 81°

c

Based on the diagram, can point D be the centroid of triangle ACF? Explain. Yes, point D is the point of intersection of segments drawn from all three vertices. Yes, DE is three-quarters of the length of the full segment. No, DE should be longer than AD. No, the ratio between AD and DE is 3:1.

d

In the triangles, TR = GE and SR = FE. If = 3.2 ft, which is a possible measure of ? 1.6 ft 3.0 ft 3.2 ft 4.0 ft

d

The proof that ΔABC ≅ ΔCDA is shown. Given: ∥ and ∥ Prove: ΔABC ≅ ΔCDA What is the missing reason in the proof? StatementsReasons1. AB ∥ CD; BC ∥ DA1. given2. Quadrilateral ABCD is a ▱2. definition of parallelogram3. AB ≅ CD; BC ≅ DA3. opposite sides of a parallelogram are ≅4. AC ≅ AC4. reflexive property5. ΔABC ≅ ΔCDA5. ? perpendicular bisector theorem Pythagorean theorem HL theorem SSS congruence theorem

d

What is the equation of the line that is parallel to the given line and passes through the point (12, −2)? y = -6/5 + 10 y = -6/5 + 12 y = -5/6 - 10 y = 5/6 - 12

d

Which composition of similarity transformations maps LMN to L'M'N'? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation a dilation with a scale factor greater than 1 and then a reflection a dilation with a scale factor greater than 1 and then a translation

d

Four points partition the directed line segment from A to B. • Point P partitions the directed line segment from A to B into a 3:4 ratio. • Point Q partitions the directed line segment from A to B into a 4:3 ratio. • Point R partitions the directed line segment from A to B into a 2:5 ratio. • Point S partitions the directed line segment from A to B into a 5:2 ratio. A number line has points A and B. A line is drawn from point A to point B. Which point will lie closest to B? P Q R S

s

Given: AB = 12AC = 6Prove: C is the midpoint of AB. Proof:We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the ________ property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments. congruence symmetric reflexive transitive

symmetric