Triangle Congruence Unit Test
Three quadrilaterals exist such that GHJK ≅ ASDF and GHJK ≅ VBNM. If MV measures 3 cm, which other segment must measure 3 cm? AF KJ FD GJ
A
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent? AAS SSS SAS HL
D
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80%
Two rigid transformations are used to map ABC to QRS. The first is a translation of vertex B to vertex R. What is the second transformation? a reflection across the line containing AB a rotation about point B a reflection across the line containing CB a rotation about point C
A
Which congruence theorem can be used to prove △WXZ ≅ △YZX? AAS ASA SAS HL
A
Given: RS bisects ∠MRQ; ∠RMS ≅ ∠RQS Which relationship in the diagram is true? ΔMNR ≅ ΔMNS by ASA ΔRMS ≅ ΔRQS by AAS ΔSNQ ≅ ΔSNM by SSS ΔQNR ≅ ΔMNR by HL
B
How can a translation and a reflection be used to map ΔHJK to ΔLMN? Translate K to N and reflect across the line containing HJ. Translate K to N and reflect across the line containing JK. Translate H to L and reflect across the line containing JK. Translate K to L and reflect across the line containing HJ.
B
Quadrilateral ABCD is translated down and left to form quadrilateral OLMN. If AB = 6 units, BC = 5 units, CD = 8 units, and AD = 10 units, what is LO? 5 units 6 units 8 units 10 units
B
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? 18 cm 20 cm 22 cm 24 cm
B
The proof that HG ≅ EG is shown. Given: G is the midpoint of KF KH ∥ EFProve: HG ≅ EG What is the missing reason in the proof? SAS ASA AAS HL
B
In the diagram, ∠J ≅ ∠M and JL ≅ MR. What additional information is needed to show ΔJKL ≅ △MNR by SAS? KL ≅ NR ∠L ≅ ∠R ∠K ≅ ∠N JK ≅ MN
D
Quadrilateral LMNO is reflected over the line as shown, resulting in quadrilateral CDAB. Given the congruency statement LMNO ≅ CDAB, which segment corresponds to ML? AB AD CD DC
D
Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is required to map DEF onto GHJ? dilation reflection rotation translation
D
Which congruence theorem can be used to prove △WXS ≅ △YZS? SSS ASA SAS HL
D
Is MNL ≅ QNL? Why or why not? Yes, they are congruent by either ASA or AAS. Yes, they are both right triangles. No, M is not congruent to NLQ. No, there are no congruent sides.
A
Is there a series of rigid transformations that could map ΔQRS to ΔABC? If so, which transformations could be used? No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations. No, ΔQRS and ΔABC are not congruent. Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C. Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.
A
The proof that MNG ≅ KJG is shown. Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG What is the missing reason in the proof? the reflexive property ASA AAS the third angle theorem
B
The proof that ΔQPT ≅ ΔQRT is shown. Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT What is the missing reason in the proof? definition of perpendicular bisector definition of congruence reflexive property substitution property
B
Two angles and the non-included side 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? SSS AAS SAS HL
B
Could ΔJKL be congruent to ΔXYZ? Explain. Yes, if JL ≅ XZ. Yes, if XZ = 10. No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle. No, because the leg of one triangle is equal in length to the leg of the other triangle.
C
The proof ABC ≅ DCB that is shown. Given: A ≅ D; CD||ABProve: ABC ≅ DCB What is the missing reason in the proof? alt. ext. s are ≅ ASA AAS corr. int. s are ≅
C
The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map MNP onto TSR? reflection only rotation only translation, then reflection translation, then rotation
C
In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles? ΔXYZ ≅ ΔTUV ΔXYZ ≅ ΔVUT No congruency statement can be made because only two angles in each triangle are known. No congruency statement can be made because the side lengths are unknown.
D
The triangles are congruent by SSS or HL. Which transformation(s) can map MNQ onto PQN? translation only reflection only rotation, then reflection rotation, then translation
D
What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem? LO ≅ LM OA ≅ MA LOA ≅ LMA LAO ≅ LAM
D
