directions: answer the following question(s). · 11 in the cartesian plane, Δabc ≅...

1 The following are true for △ LMN.

m∠L = 45°; m∠M = 55°; LM = 7 inches

Triangle LMN is reflected across the x-axis andthen rotated about its center to form its image,△ L′M′N′.

Which statement is true?

A. m∠N′ = 73°B. m∠M′ = 45°C. m∠M′ = 170°D. m∠N′ = 80°

2 In the graph, △ ABC ≅ △ A′B′C′ .

Which transformation maps △ ABC onto

△ A′B′C′ ?

A. Reflect about x-axis and then reflect about they-axis.

B. Reflect about y = x and then reflect about the y-axis.

C. Rotate 90° clockwise and then reflect about thex-axis.

D. Rotate 90° counterclockwise and then reflectabout the y‑axis.

3 Decide if each statement contains enoughinformation to show that two triangles arecongruent. Drag and drop Yes or No into the boxnext to each statement.

Web Only Interaction

4 Two triangular figures are graphed below.

Explain how rigid motions and the SSS trianglecongruence theorem may be used to prove thecongruence of the figures.

Ch. 7 Chapter Review Assessment ID: dna.42020 ib.1969005

Directions: Answer the following question(s).

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5 △ ABC and segment A′B′ are shown below.

A rigid motion is performed so that segment ABmaps to A′B′ . In order for △ A′B′C′ to becongruent to △ ABC by the SSS congruencepostulate, what rigid motion is performed, andwhere is point C′ located?

A. 180° rotation about the origin; C′(4, 3)B. translation 6 units right, 2 units down; C′(2, − 5)C. reflection over the y-axis; C′(4, 2)D. 180° rotation about the origin; C′(4, 2)

6 Look at the two triangles on the coordinate gridbelow.

Two students, Jerry and Teresa, are trying tofigure out how many transformations it would taketo move triangle ABC onto triangle A'B'C'.

Jerry thinks it will take two transformations tomap triangle ABC onto triangle A'B'C'. Teresathinks it will take three or more transformations tomap triangle ABC onto triangle A'B'C'.

Which student is correct? Explain how you knowthat student is correct. Make sure you include thetransformations.

Type your answers in the box below.Web Only Interaction

7 In△ XYZ , XY = 7in , YZ = 5in , and XZ = 4in .This triangle is reflected across the x-axis toresult in △ X′Y′Z′ . Which is true?

A. X′Z′ = 2inB. X′Y′ = 7inC. Y′Z′ = 10inD. Perimeter of △ X′Y′Z′ = 32in




8 Quadrilateral ABCD is transformed to A'B'C'D'.

Which rule describes this transformation?

A. (x, y) (x + 6, y + 3)B. (x, y) (x − 6, y − 3)C. (x, y) (x + 3, y + 6)D. (x, y) (x − 3, y − 6)

9 The wheel below is rotated counterclockwiseabout the center, point C.

What is the angle of rotation that maps point A topoint B?

A. 36°

B. 72°

C. 288°

D. 324°

10 In the figure below,△ ABC ≅ △ A′B′C′ .

Which transformation maps △ ABC onto△ A′B′C′ ?

A. Rotate △ ABC 180° counterclockwise about theorigin.

B. Translate △ ABC 3 units left and 6 units down.

C. Reflect △ ABC in the y-axis, then rotate it 90°counterclockwise about the origin.

D. Reflect △ ABC in the x-axis.




11 In the Cartesian plane, ΔABC ≅ ΔA′B′C′ .

Which transformations map ΔABC to ΔA′B′C′ ?

A. Reflect about the y-axis and then rotate 90°clockwise.

B. Reflect about the y-axis and then rotate 180°counterclockwise.

C. Reflect about the x-axis and then rotate 90°clockwise.

D. Reflect about the x-axis and then rotate 180°counterclockwise.

12 Trina draws △ ABC on a coordinate plane. Shethen draws △ A′B′C′ such that each vertex ismoved x- units to the right and y- units abovetheir original positions. Explain why the triangleretains its original shape after the translation.

13 A triangle ABC has vertices at the points(2, 3), (1, 1), and (2, 1). A new triangle A'B'C' isgenerated with vertices B' and C' at the points(0, 1) and ( − 1, 1). Assuming triangle A'B'C' iscongruent to triangle ABC, what are thecoordinates of the vertex A'?

A. ( − 1, 3)B. (1, − 3)C. (2, − 3)D. ( − 2, 3)




14 Look at the two triangles on the coordinate gridbelow.

Which statement best describes the relationshipbetween the two triangles?

A. △ ABC is reflected and then translated to create△ A′B′C′ , so they are similar, but notcongruent, triangles.

B. △ ABC is rotated and then dilated to create△ A′B′C′ , so they are similar triangles.

C. △ ABC is reflected and then translated to create△ A′B′C′ , so they are congruent triangles.

D. △ ABC is dilated to create △ A′B′C′ , so theyare similar, but not congruent, triangles.

15 The coordinate plane shows the design for partof a mall.

The eating area will be rotated 90° clockwiseabout the origin and then reflected across the y-axis. Which shows the final location of the eatingarea?

A.

B.

C.

D.




16 The coordinate plane shows the locations ofFigure A and Figure B.

Describe a transformation or series oftransformations that prove Figure B is congruentto Figure A.

17 Each coordinate plane below shows the graph oftwo figures, labeled "1" and "2." In each graph,figure 2 was created by using a rigid motion totransform figure 1.

Which rigid motion was used to transform thefigure in each graph? Drag and drop the name ofeach graph under the description of the rigidmotion used.


18 On the coordinate plane below, figure 1 has beentransformed to create figure 2.

Use the drop-down arrows to choose theresponse that makes each statement true.


19 Triangle △ ABC is shown below.

Using rigid motions, triangles △ DEF , △ GHI ,and △ JKL , shown below, can each be provencongruent to △ ABC .

Drag and drop the label for the appropriatetheorem to justify the congruence. Someresponses may not be used.





20 Triangles ABC and DEF are shown below.

Which triangle congruency theorem can be usedto show that triangle DEF is congruent to triangleABC?

A. SSS

B. AAS

C. ASA

D. SAS

21 Maisie has △ ABC graphed in a coordinateplane. She translates the triangle to obtain△ DEF . Finally, she concludes the trianglesmust be congruent using the following reasoning.

Since translation is a rigid motion, Iknow all three sides of △ ABC arecongruent to all three sides of △ DEF .This means the triangles are congruent.

Which congruence postulate is Maisie using forher conclusion?

A. ASA

B. SAS

C. HL

D. SSS

22 △ ABC was transformed to create △ XYZ , bothshown below. Kelly thinks that the transformationwas a rigid motion, but she is not certain.

Knowing which of these would allow her to usethe SAS congruency postulate to prove that arigid motion occurred?

A. AB ≅ XY , BC ≅ YZ , ∠C ≅ ∠Z

B. AB ≅ XY , AC ≅ XZ , ∠A ≅ ∠X

C. ∠A ≅ ∠X , ∠B ≅ ∠Y , ∠C ≅ ∠Z

D. AB ≅ XY , BC ≅ YZ , ∠A ≅ ∠X

23 △ PQR is transformed to create △ P′Q′R′ . Bretthas a ruler and is able to measure the sidelengths to determine that PQ ≅ P′Q′, QR ≅ Q′R′ ,and PR ≅ P′R′ . He does not have a protractor sohe is unable to measure the angles in thetriangles. Which statement is TRUE?

A. The triangles are the same size but not thesame shape.

B. The transformation that occurred did not useonly rigid motions.

C. The triangles are the same shape but not thesame size.

D. The transformation that occurred used only rigidmotions.




24 Look at the triangles shown below.

If XY ≅ MQ , XZ ≅ MA , and YZ ≅ QA , whichrigid motions can be used to map△ XYZ onto△ MQA ?

A. a translation according to the rule(x, y) (x + 5, y + 2) followed by a rotation of 90°counterclockwise about the origin

B. a rotation of 270° counterclockwise about theorigin followed by a translation according to therule (x, y) (x − 2, y − 5)

C. a translation according to the rule(x, y) (x + 2, y + 5) followed by a rotation of 90°counterclockwise about the origin

D. a rotation of 270° counterclockwise about theorigin followed by a translation according to therule (x, y) (x − 5, y − 2)


ΔABC is rotated 180° about the origin. Whichconclusion is correct?

A. △ ABC ≅ △ EFD , because∠BAC ≅ ∠FED, AB ≅ EF, ∠ABC ≅ ∠EFD .

B. △ ABC is similar but not congruent to△ EFD ,because∠BAC ≅ ∠FED, AB ≅ EF, ∠ABC ≅ ∠EFD .

C. △ ABC ≅ △ EDF , because∠BAC ≅ ∠DEF, AB ≅ ED, ∠ABC ≅ ∠EDF .

D. △ ABC is similar but not congruent to△ EDF ,because∠BAC ≅ ∠DEF, AB ≅ ED, ∠ABC ≅ ∠EDF .





Given that △ QXT ≅ △ CPM, which statementis TRUE?

A. △ QXT is rotated 180° about the origin to give△ CPM , so XT ≅ PM , QT ≅ CP , andQX ≅ CM.

B. △ QXT is reflected over the line y = x to give△ CPM , so XT ≅ PM , QT ≅ CP , andQX ≅ CM.

C. △ QXT is reflected over the line y = x to give△ CPM, so XT ≅ PM , QT ≅ CM , and QX ≅ CP.

D. △ QXT is rotated 180° about the origin to give△ CPM , so XT ≅ PM , QT ≅ CM , andQX ≅ CP.

27 △ ABC and△ DEF are shown in the graphbelow.

If△ ABC is reflected across the line y = x, whichstatement is TRUE?

A. △ ABC ≅ △ DEF because AB ≅ DE ,m∠ABC ≅ m∠DEF , and BC ≅ EF .

B. △ ABC ∼ △ DEF but the triangles are notcongruent because AB ≅ DE ,m∠ABC ≅ m∠DEF , and BC ≅ EF .

C. △ ABC ∼ △ FDE but the triangles are notcongruent because AB ≅ FD ,m∠ABC ≅ m∠FDE , and BC ≅ DE .

D. △ ABC ≅ △ FDE because AB ≅ FD ,m∠ABC ≅ m∠FDE , and BC ≅ DE .




28 In the figure below,△ DEF is the result of rotating△ ABC and then reflecting it across the y-axis.

If it is known that ∠B ≅ ∠E , what other pieces ofinformation would be needed to show that△ ABC ≅ △ DEF ?

A. AC ≅ FE and BC ≅ DF

B. AB ≅ DE and BC ≅ DF

C. AB ≅ DE and BC ≅ EF

D. ∠B ≅ ∠D and ∠C ≅ ∠F

29 Look at the two triangles graphed below.

Explain a series of transformations that map onetriangle onto the other and how the SAS trianglecongruence theorem follows from thetransformations.




30 The map of two walking trails in a naturepreserve is shown on the grid below as the pre-image and image of a reflection of the north trail,△ ABC , over the x-axis onto △ ADC , the southtrail.

A ranger wants to prove that the two trails arecongruent. Since it is known that AC ≅ AC , whatother pieces of information would be needed toshow that △ ABC and △ ADC are congruent?

A. ∠BCA ≅ ∠DCA and AB ≅ AD

B. ∠BAC ≅ ∠DAC and ∠ABC ≅ ∠DBC

C. ∠ABC ≅ ∠DBC and BC ≅ DC

D. ∠BAC ≅ ∠DAC and ∠BCA ≅ ∠DCA

31 A homeowner has two different sets of triangulartiles, green tiles and blue tiles. Which of thesewould prove that the green and blue tiles arecongruent?

A. determining if the two longest sides of eachcolor tile, plus either of the other pairs ofcorresponding sides, are congruent

B. determining if all three pairs of correspondingsides of the green and blue tiles are congruent

C. determining if any two pairs of correspondingangles of each color tile are congruent

D. determining if two pairs of corresponding sides,plus any pair of corresponding angles, on thegreen and blue tiles are congruent

32 In the figure below, △ ABC has beentransformed by a series of rigid motions toproduce △ DEF .

Drag and drop the correct choices to completethis description of the transformation. Then, dragand drop the correct response that makes thefinal statement true.





33 In the figure below, △ PQR has been translatedto produce △ P′Q′R′.

Which statement best describes one way toprove that the triangles are congruent?

A. Since translation is a similarity transformation,we know that PR ≅ P′R′, ∠P ≅ ∠P′, and∠R ≅ ∠R′. This means that △ PQR ≅ △ P′Q′R′by SAA.

B. Since translation is a similarity transformation,we know that PR ≅ P′R′, ∠P ≅ ∠P′, and∠R ≅ ∠R′. This means that △ PQR ≅ △ P′Q′R′by ASA.

C. Since translation is a rigid motion, we know thatPR ≅ P′R′, ∠P ≅ ∠P′, and ∠R ≅ ∠R′. This meansthat △ PQR ≅ △ P′Q′R′ by SAA.

D. Since translation is a rigid motion, we know thatPR ≅ P′R′, ∠P ≅ ∠P′, and ∠R ≅ ∠R′. This meansthat △ PQR ≅ △ P′Q′R′ by ASA.

34 In this diagram,△ ABC has been mapped onto△ A′B′C′ by a series of rigid motions.

Which statement best describes one way toprove that the triangles are congruent?

A. Rigid motions preserve distance and anglemeasure. This means that AB ≅ A′B′ ,BC ≅ B′C′ , and ∠B ≅ ∠B′ , so the triangles arecongruent by SAS.

B. Measure the areas of△ ABC and△ A′B′C′ toconfirm that their areas are equal. This meansthat AB ≅ A′B′ , BC ≅ B′C′ , and AC ≅ A′C′ , sothe triangles are congruent by SSS.

C. Rigid motions preserve distance and anglemeasure. This means that AB ≅ A′B′ ,BC ≅ B′C′ , and ∠A ≅ ∠A′ , so the triangles arecongruent by SAS.

D. Measure the perimeters of△ ABC and△ A′B′C′to confirm that their perimeters are equal. Thismeans that AB ≅ A′B′ , BC ≅ B′C′ , andAC ≅ A′C′ , so the triangles are congruent bySSS.




35 Enrico did a geometry investigation using adrawing application on a computer. He drew△ DEF, then moved it to produce △ D′E′F′, asshown below.

Enrico measured the sides and found thatDE = D′E′, EF = E′F′, and DF = D′F′. Which isthe best conclusion to draw from Enrico'sgeometry investigation?

A. Since the side lengths of the triangle did notchange, △ D′E′F′ is the result of a dilation. Thismeans that △ DEF ≅ △ D′E′F′, and suggeststhat AAA is a valid criterion for trianglecongruence.

B. Since the side lengths of the triangle did notchange, △ D′E′F′ is the result of a rigid motion.This means that △ DEF ≅ △ D′E′F′, andsuggests that SSS is a valid criterion for trianglecongruence.

C. Since the side lengths of the triangle did notchange, △ D′E′F′ is the result of a rigid motion.This means that △ DEF ≅ △ D′E′F′, andsuggests that AAA is a valid criterion for trianglecongruence.

D. Since the side lengths of the triangle did notchange, △ D′E′F′ is the result of a dilation. Thismeans that △ DEF ≅ △ D′E′F′, and suggeststhat SSS is a valid criterion for trianglecongruence.

36 A design for a new hockey team uniform containstwo triangles.

● One triangle has vertices at A 1, − 1 ,B 3, 5 , and C 5, 3 .

● When this triangle is reflected about the liney = − x , the result is the second triangle.

● The second triangle has vertices atA(1, − 1) , D( − 3, − 5) , and E( − 5, − 3) .

Which of the following BEST explains why thetwo triangles in the design are congruent, usingthe ASA postulate?

A. Δ ABC ≅ Δ ADE because AB ≅ AD ,∠ABC ≅ ∠ADE , and ∠ACB ≅ ∠AED .

B. Δ ABC ≅ Δ AED because AB ≅ AE ,∠ABC ≅ ∠AED , and ∠ACB ≅ ∠ADE .

C. Δ ABC ≅ Δ ADE because BC ≅ DE ,∠ABC ≅ ∠ADE , and ∠ACB ≅ ∠AED .

D. Δ ABC ≅ Δ AED because BC ≅ DE ,∠ABC ≅ ∠AED , and ∠ACB ≅ ∠ADE .




37 In the diagram below, △ PQR has beentransformed to produce △ P′Q′R′ .

Use the drop-down arrows to choose theresponse that makes each statement true.


38 Use the drop-down arrows to choose theresponse that makes each statement true.


39 Trevor is designing the landscaping for a newhome. His design includes two triangular lawns,△ PQR and △ STU. In Trevor's design, PQ ≅ ST,PR ≅ SU, QR ≅ TU, ∠P ≅ ∠S, ∠Q ≅ ∠T, and∠R ≅ ∠U. Which statements must be true?Choose all that are correct.

A. There exists a rotation of △ PQR that produces△ STU .

B. There exists a series of one or more rigidmotions of △ PQR that produces △ STU .

C. ∠T ≅ ∠U

D. △ PQR can be reflected across a certain line toproduce △ STU .

E. △ PQR ≅ △ STU

F. PQ ≅ QR

40 A machinist must cut two triangular openings intoa piece of sheet metal. The engineer designingthe cutting tool has drawn the relative positions ofthe triangles on a print represented by the gridbelow.

Which statements are correct? Select all thatapply.

A. The triangles are congruent.

B. CA = FEC. AB = DED. The corresponding angle measures of the two

triangles are congruent, but the correspondingside lengths are not congruent.

E. The triangles are similar but not congruent.

F. ΔABC and ΔDEF are related by rigid motions.



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directions: answer the following question(s). · 11 in the cartesian plane, Δabc ≅...

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