F - MI1S1 CT

In the diagram, △ABC ≅ △WRS. What is the perimeter of △WRS?

12 units

Rectangle ABCD is congruent to rectangle URST. What is the area of rectangle URST? ___ sq. mm

135

Triangle TRS is rotated about point X, resulting in triangle BAC. If AB = 10 ft, AC = 14 ft, and BC = 20 ft, what is RS? __ ft

14

In the diagram, ΔPMN ≅ ΔQSR. If QR = 20 in., RS = 7 in., and SQ = 24 in., what is PN? __ in.

20

Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC. If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?

20 cm

Triangle ABC is congruent to triangle XYZ. In ΔABC, AB = 12 cm and AC = 14 cm. In △XYZ, YZ = 10 cm and XZ = 14 cm. What is the perimeter of ΔABC?

36 cm

For the triangles to be congruent by HL, what must be the value of x?

4

Point H is the midpoint of side FK. For the triangles to be congruent by SSS, what must be the value of x? x = _

6

Triangle QRP is congruent to triangle YXZ. What is the perimeter of triangle YXZ? What is the perimeter of triangle YXZ? ___inches

6.4

Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?

A

Which of these triangle pairs can be mapped to each other using two reflections?

A

Which shows two triangles that are congruent by AAS?

A

Triangles ABC and DEF have the following characteristics: ∠B and ∠E are right angles ∠A ≅ ∠D BC ≅ EF Which congruence theorem can be used to prove △ABC ≅ △DEF?

AAS

Given: ABC and FGH are right angles; BA||GF; BC ≅ GH Prove: ABC ≅ FGH Step 1: We know that ABC ≅ FGH because all right angles are congruent. Step 2: We know that BAC ≅ GFH because corresponding angles of parallel lines are congruent. Step 3: We know that BC ≅ GH because it is given. Step 4: ABC ≅ FGH because of the ___ ___________ _________.

AAS congruence theorem

Quadrilateral ABCD is rotated 145° about point T. The result is quadrilateral A'B'C'D'. Which congruency statement is correct?

ABCD ≅ A'B'C'D'

Line segments AD and BE intersect at C, and triangles ABC and DEC are formed. They have the following characteristics: ∠ACB and ∠DCE are vertical angles ∠B ≅ ∠E BC ≅ EC Which congruence theorem can be used to prove △ABC ≅ △DEC?

ASA

Which of these triangle pairs can be mapped to each other using a reflection and a translation?

B

Which of these triangle pairs can be mapped to each other using a single translation?

D

Consider the diagram. Which congruence theorem can be used to prove △ABR ≅ △RCA?

HL

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments ___ and __ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

MS and QS

The figure was created by repeatedly reflecting triangle NMP. What is the perimeter of the figure?

NOT 36 in.

The proof ABC ≅ DCB that is shown. Given: A ≅ D; CD||AB Prove: ABC ≅ DCB What is the missing reason in the proof?

NOT ASA

Which shows two triangles that are congruent by the SSS congruence theorem?

NOT B

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

NOT C

Consider the diagram. The congruence theorem that can be used to prove △LON ≅ △LMN is

NOT HL.

Which explains whether ΔFGH is congruent to ΔFJH?

NOT They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.

In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?

NOT ∠J ≅ ∠M

Given: ∠XWU ≅ ∠ZVT; ∠ZTV ≅ ∠XUW; TU ≅ VW Which relationship in the diagram is true?

NOT △RYZ ≅ △XZY by SAS

If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not?

No, there is not enough information given.

Consider the diagram. The congruence theorem that can be used to prove △MNP ≅ △ABC is

SAS

Given: bisects ∠BAC; AB = AC Which congruence theorem can be used to prove △ABR ≅ △ACR?

SAS

Two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?

SAS

Which congruence theorem can be used to prove △BDA ≅ △BDC?

SSS

How can a translation and a rotation be used to map ΔHJK to ΔLMN?

Translate K to N and rotate about K until HK lies on the line containing LN.

Can a translation and a reflection map QRS to TUV? Explain why or why not.

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.

Two rigid transformations are used to map ΔABC to ΔXYZ. The first is a translation of vertex A to vertex X. What is the second transformation?

a reflection across the line containing AB

Which rigid transformation would map MZK to QZK?

a reflection across the line containing ZK

Two rigid transformations are used to map JKL to MNQ. The first is a translation of vertex L to vertex Q. What is the second transformation?

a rotation about point L

How can ΔWXY be mapped to ΔMNQ? First, translate vertex W to vertex M. Next, reflect ΔWXY across the line containing ____ _______ __.

line segment WX

Triangle ABC is congruent to A'BC' by the HL theorem. What single rigid transformation maps ABC onto A'BC'?

reflection

The triangles are congruent by SSS or HL. Which transformation(s) can map PQR onto STU?

reflection, then translation

The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map ABC onto FED?

reflection, then translation

The triangles shown are congruent by the SSS congruence theorem. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations?

rotation, then translation, then reflection

The triangles are congruent by the SSS congruence theorem. Which transformation(s) can map BCD onto WXY?

translation, then rotation

Triangle CDE is translated down and to the right, forming triangle C'D'E'. Which congruency statement is correct?

ΔDCE ≅ ΔD'C'E'

The proof that ΔACB ≅ ΔECD is shown. Given: AE and DB bisect each other at C. Prove: ΔACB ≅ ΔECD What is the missing statement in the proof?

∠ACB ≅ ∠ECD

Given: ∠GHD and ∠EDH are right; GH ≅ ED Which relationship in the diagram is true?

△GHD ≅ △EDH by SAS