Primavera Online - Geometry A - Unit 2

(Exam 2) △ABC can be translated onto △DEF. Therefore, the triangles are congruent. Based on this information, what other statement is true? https://assets.learnosity.com/organisations/625/asset/media/1158060

∠BAC≅∠EDF

(6.2) The following transformation maps △ABC to △A′B′C′. (x,y)↦(x−4,y+1) Which answer correctly describes the transformation applied to △ABC?

△ABC is moved 4 units left and 1 unit up to create △A′B′C′.

(10.1) https://assets.learnosity.com/organisations/625/asset/media/1157857 Which statements about the triangles are true?

△ABC≅△DEF by the SAS Congruence Postulate. A rotation will map △ABC onto △DEF.

(09) https://assets.learnosity.com/organisations/625/asset/media/1157893 Which statement about △ABC and △DFE is true?

△ABC≅△DFE by the SSS Congruence Postulate.

(08) https://assets.learnosity.com/organisations/625/asset/media/1157590 Which of the two triangles are congruent?

△DEF △ABC

(6.1) In the following graph, triangle ABC has been transformed in three different ways, resulting in triangle DEF, triangle GHI, and triangle JKL. https://assets.learnosity.com/organisations/625/asset/media/1158133 Match each triangle with the single transformation that maps △ABC to that triangle.

△DEF to rotation. △GHI to translation. △JKL to reflection.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158056 Which transformations map polygon ABCD to itself?

A reflection in the x-axis. A 180∘ degrees clockwise rotation about origin. A reflection in the y-axis.

(7.2) https://assets.learnosity.com/organisations/625/asset/media/1157552 Which of the following transformations map polygon ABCD to itself?

A reflection in the x-axis. A reflection in the y-axis. A 180 degrees clockwise rotation about the origin. A reflection in the line y=x. A 90∘ clockwise rotation about the origin.

(06) https://assets.learnosity.com/organisations/625/asset/media/1157546 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.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158059 Which series of transformations shows that rectangle ABCD is congruent to rectangle A′B′C′D′ by superimposing one onto the other?

A reflection in the y-axis, followed by a translation 1 unit down.

(06) The following mapping statements describe the transformation of the vertices of △ABC to the vertices of its image, △A′B′C′ A(0,2)↦A′(0,2) B(2,9)↦B′(−2,9) C(4,2)↦C′(−4,2) What is the correct description of the transformation that maps triangle ABCto triangle A′B′C′?

A reflection in the y-axis.

(07) https://assets.learnosity.com/organisations/625/asset/media/1157555 Which transformation maps polygon ABCD to itself?

A reflection in the y-axis.

(09) https://assets.learnosity.com/organisations/625/asset/media/1157891 Which series of transformations correctly maps triangle ABC to triangle A′B′C′?

A reflection in the y-y-axis, followed by a translation 33 units down.

(11.1) https://assets.learnosity.com/organisations/625/asset/media/1157819 Which transformation will show that △ABD≅△ABC?

A reflection over AB.

(8.2) 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.

(9.1) https://assets.learnosity.com/organisations/625/asset/media/1157807 Which transformation shows △ABC≅△DEF, by mapping △ABC to △DEF?

A reflection.

(08) https://assets.learnosity.com/organisations/625/asset/media/1157589 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.

(6.3) https://assets.learnosity.com/organisations/625/asset/media/1158143 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 3 units down.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158071 Which transformation can be used to show that △PSR≅△UPT?

A rotation around a point in the center of the triangles.

(Exam 2) Draw a line that goes through point B. Draw a line that intersects the first line, but not at point B. Measure the distance of point B to the intersection. On the second line, draw point B′ that is the same distance from the intersection as point B. Which of the following answers describes the transformation of point B to point B′?

A rotation.

(06) https://assets.learnosity.com/organisations/625/asset/media/1157536 Which answer correctly describes the transformation from the preimage to the image?

A translation 10 units left and 8 units down.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158066 Which measurements allow you to determine that the triangles are congruent?

AB=3 BC=3.6 AD=3 CD=3.6

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158064 Which answer needs to be true to be able to use the SSS Congruence Postulate to prove △ABC≅△DBC?

AB≅DB and AC≅DC

(8.2) https://assets.learnosity.com/organisations/625/asset/media/1157574\ Based on this information, what other statement is true?

AB≅DE

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158062 If quadrilateral ABCD is reflected to produce its image, quadrilateral EBGH, which statements are true?

AB≅EB ∠D≅∠H quadrilateral ABCD≅quadrilateral EBGH

(9.2) https://assets.learnosity.com/organisations/625/asset/media/1157809 Which answers need to be true to be able to use the SSS Congruence Postulate to prove △ABC≅△DEF?

AC≅DF AB≅DE BC≅EF

(8.1) https://assets.learnosity.com/organisations/625/asset/media/1157566 Triangle ABC is translated 1 unit right and 3 units down to produce its image, triangle DEF. Which statements are true?

AC≅DF ∠B≅∠E △ABC≅△DEF

(06) The coordinates of the vertices of trapezoid ABCD are A(−1,4) B(0,2), C(1,2), and D(2,4). https://assets.learnosity.com/organisations/625/asset/media/1157541 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

(6.3) 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

(10.2) Given: BC≅CD AC bisects ∠BCD. Prove: △ABC≅△ADC https://assets.learnosity.com/organisations/625/asset/media/1157861 Match each statement in the proof with the correct reason.

https://postimg.cc/HVGtyqZG

(10.3) https://assets.learnosity.com/organisations/625/asset/media/1157875 AC=75 m AE=80 m AD=75 m DE=125 m AB=80 m To find the width of the sinkhole, find the distance between points C and B. What is the distance across the sinkhole?

125 m

(10) https://assets.learnosity.com/organisations/625/asset/media/1157927 What is the measure of side FD?

3.4 units.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158070 In the triangles, AB=3 cm, AD=3 cm, and AE=4 cm. To prove △ABC≅△ADE by the SAS Congruence Postulate, AC must equal _[blank]_ cm.

4

(11.3) https://assets.learnosity.com/organisations/625/asset/media/1157826 If △ABC≅△DEF, what is the length of DF?

4.5

(9.3) https://assets.learnosity.com/organisations/625/asset/media/1157815 If △ABC≅△KLM, then m∠B= [blank]∘.

48

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1234150 What is the measure of EF?

5.1 units.

(7.2) https://assets.learnosity.com/organisations/625/asset/media/1157553 What is the angle of rotational symmetry for the figure?

51.4∘

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158053 Which transformation maps triangle ABC to triangle A′B′C′?

A 180∘ rotation about the origin.

(Exam 2) Which series of rigid transformations could be used to show that △ABC≅△DEF? https://assets.learnosity.com/organisations/625/asset/media/1158063

A 90∘ clockwise rotation about point C and a reflection.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158054 Which series of transformations correctly maps parallelogram ABCD to parallelogram A′B′C′D′?

A 90∘ counterclockwise rotation about the origin, followed by a reflection in the x-axis.

(6.1) https://assets.learnosity.com/organisations/625/asset/media/1158135 Which answer choices correctly describe the rotation that maps figure ABCD to figure A′B′C′D′?

A 90∘ counterclockwise rotation about the origin. A 270∘ clockwise rotation about the origin.

(07) 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?

A reflection over line EH. A reflection over line CM. A rotation of about 51.4∘ about its center. A rotation of about 205.6∘ about its center.

(10) https://assets.learnosity.com/organisations/625/asset/media/1157899 What is true about △ABC and △DEF? How do you know?

A rotation can map △ABC onto △DEF. △ABC≅△DEF A rotation is a rigid transformation.

(08) https://assets.learnosity.com/organisations/625/asset/media/1157591 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/

(8.1) https://assets.learnosity.com/organisations/625/asset/media/1157564 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.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158061 If △ABC≅△DEF, which transformations maps △ABC to △DEF?

A translation, then a reflection.

(06) Draw a line segment with endpoints M and R. Now draw a parallel line segment that is the same length as MR line with the endpoints M′ and R′ in the same order. Which answer correctly describes the transformation from MR line to M′R′ line?

A translation.

(10.2) https://assets.learnosity.com/organisations/625/asset/media/1157860 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.

A: No B: three pairs of corresponding sides, but no pairs of corresponding angles C: it cannot be proven that the triangles are congruent using the SAS Congruence Postulate

(9.1) https://assets.learnosity.com/organisations/625/asset/media/1157808 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.

(09) A reflection and a translation have been applied to triangle ABC such that side AB coincides with side DE, side BC coincides with side EF, and side AC coincides with side DF. https://assets.learnosity.com/organisations/625/asset/media/1157892 What is true about angle C?

Angle C coincides with angle F, because the respective sides that form each of the angles coincide.

(09) A truss, shown below, needs to be made of two congruent triangles. The length of AC is 4 meters (m) and the length of BD is 3 m. https://assets.learnosity.com/organisations/625/asset/media/1157895 Which measurements must be known to determine that the triangles are congruent?

BC=3 m AD=4 m

(09) https://assets.learnosity.com/organisations/625/asset/media/1157896 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

(10.3) https://assets.learnosity.com/organisations/625/asset/media/1157873 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.

(10) https://assets.learnosity.com/organisations/625/asset/media/1157928 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?

BD=8 CD=8

(11.2) https://assets.learnosity.com/organisations/625/asset/media/1157821 Grace states that she can use the ASA Congruence Theorem to prove the given triangles are congruent. Is she correct? Why or why not?

Grace is incorrect because there are no pairs of corresponding angles with the same measures.

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158067 A reflection over KM can be applied to △KLM so that LM coincides with NM and ∠LMK coincides with ∠NMK. How can you be sure that LK≅NK?

If LM corresponds to NM, then the endpoints L and K correspond to the endpoints N and K.

(07) https://assets.learnosity.com/organisations/625/asset/media/1157554 A reflection over which of the following line segments will carry rectangle PQRS onto itself?

JK MN

Lesson 10

Lesson 10

Lesson 11

Lesson 11

Lesson 6

Lesson 6

Lesson 7

Lesson 7

Lesson 8

Lesson 8

Lesson 9

Lesson 9

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158057 Part A: What is the angle of rotational symmetry of the figure? Part B: Where is the center of symmetry?

Part A: 120∘ Part B: At approximately (6,4).

(6.1) 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.

(7.1) https://assets.learnosity.com/organisations/625/asset/media/1157551 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.

(08) 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.

(10) https://assets.learnosity.com/organisations/625/asset/media/1157901 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.

(06) https://assets.learnosity.com/organisations/625/asset/media/1157533 Triangle ABC is reflected over line l 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′?

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.

(10.1) https://assets.learnosity.com/organisations/625/asset/media/1157858 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.

(9.3) https://assets.learnosity.com/organisations/625/asset/media/1157816 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 XY, XZ≅YZ, and WZ is congruent to itself. Then, by the SSS Congruence Postulate, △XWZ≅△YWZ.

Unit 2 Exam

Unit 2 Exam

(07) https://assets.learnosity.com/organisations/625/asset/media/1157557 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]_.

blank A: O blank B: 60∘

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158055 Quadrilateral ABCD _[blank A]_ map onto itself using a reflection because it has _[blank B]_ line(s) of symmetry. Match blank A and blank B to the word that correctly fills in each blank.

blank A: does blank B: Wrong: two Possibly right: four

(11.2) Given: ∠D≅∠B AD≅AB Prove: △ADE≅△ABC https://assets.learnosity.com/organisations/625/asset/media/1157822 Match each statement in the proof with the correct reason.

https://postimg.cc/Cd6ssp04

(09) Given: AC≅AD AB bisects CD. Prove: △ABC≅△ABD https://assets.learnosity.com/organisations/625/asset/media/1157894

https://postimg.cc/N5nw1y4L

(10) Given: AC≅AE AB≅AD ∠CAB is a rotation of ∠EAD. Prove: △ABC≅△ADE https://assets.learnosity.com/organisations/625/asset/media/1157926 Match each statement in the proof to the correct reason.

https://postimg.cc/YjQ1yMk8 Switch congruent angles and vertical angles.

(9.2) Given: AC≅AD AB bisects CD. Prove: △ABC≅△ABD https://assets.learnosity.com/organisations/625/asset/media/1157811

https://postimg.cc/k6XNJHK6

(6.1) Match each type of transformation with the correct description of that transformation.

https://postimg.cc/njFJrcPF

(6.2) Select two of the following mapping statements that are the result of the same translation.

(−1,2)↦(2,−3) (2,−3)↦(5,−8)

(Exam 2) Which two of the following mapping statements describe the same translation?

(−3,7)↦(−9,10) (1,−5)↦(−5,−2)

(8.2) https://assets.learnosity.com/organisations/625/asset/media/1157573 Which triangle is not congruent to the other three triangles?

Triangle D.

(06) https://assets.learnosity.com/organisations/625/asset/media/1157539 The following mapping statements describe the transformation of the vertices of the quadrilateral. A(−3,2)↦A(−1,0) B(−2,2)↦B′(0,0) C(−2,1)↦C′(0,−1) D(−3,1)↦D′(−1,−1) Which function rule correctly describes the transformation from quadrilateral ABCD to quadrilateral A′B′C′D′?

(x,y)↦(x+2,y−2)

(6.2) https://assets.learnosity.com/organisations/625/asset/media/1157370 The transformation takes each point (x,y) to a new coordinate (x′,y′). Which function correctly describes the transformation?

(x,y)↦(−x,y)

(11.3) https://assets.learnosity.com/organisations/625/asset/media/1157827 If m∠D=35∘, m∠B=35∘, AD=3 inches, and AB=3 inches, are the two swatches congruent? How do you know?

By the Reflexive Property of Congruence, ∠A≅∠A, so the swatches are congruent by the ASA Congruence Theorem. Yes, the swatches are congruent..

(Exam 2) https://assets.learnosity.com/organisations/625/asset/media/1158069 Carlos states that the SAS Congruence Postulate can be used to prove the triangles are congruent. Is he correct? Why?

Carlos is correct because there is one pair of corresponding congruent angles included by two pairs of corresponding congruent sides.

(10) https://assets.learnosity.com/organisations/625/asset/media/1157900 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.

(Exam 2) Given: C is the midpoint of AD. ∠BAC≅∠EDC Prove: △BAC≅△EDC https://assets.learnosity.com/organisations/625/asset/media/1158072 https://postimg.cc/ftqqd35c Stephanie and Miranda disagree about which reason goes in the blank for Statement 7. Stephanie states that the missing reason is the ASA Congruence Theorem, but Miranda says the missing reason is the SAS Congruence Postulate. Which student, if either, is correct? Why?

Stephanie is correct. The proof shows that two pairs of corresponding angles and the included sides are congruent.

(6.1) https://assets.learnosity.com/organisations/625/asset/media/1158136 Which statements are true about the transformation that maps triangle ABC to triangle A′B′C′?

The transformation preserves side lengths and angle measures. The transformation is a rigid transformation. Triangle A′B′C′ is the result of a reflection.