Triangle Congruence Unit Test
Questions and Answers
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 - answer A
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 - answer B
Which congruence theorem can be used to prove △WXS ≅ △YZS?
SSS
ASA
SAS
HL - answer D
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 - answer B
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 - answer D
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. - answer B
Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is
required to map DEF onto GHJ?
dilation
reflection
rotation
translation - answer D
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 - answer B
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 - answer 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 - answer D
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. -
answer D
Could ΔJKL be congruent to ΔXYZ? Explain.
Questions and Answers
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 - answer A
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 - answer B
Which congruence theorem can be used to prove △WXS ≅ △YZS?
SSS
ASA
SAS
HL - answer D
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 - answer B
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 - answer D
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. - answer B
Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is
required to map DEF onto GHJ?
dilation
reflection
rotation
translation - answer D
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 - answer B
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 - answer 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 - answer D
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. -
answer D
Could ΔJKL be congruent to ΔXYZ? Explain.
