AnswersGeometryTriangle Congruence

Triangle Congruence — Test Answers

25 verified answers
1
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Could triangle JKL be congruent to triangle XYZ ? Explain.

A
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
B
No, because the leg of one triangle is equal in length to the leg of the other triangle.
C
Yes, if line segment JL is congruent to line segment XZ .
D
Yes, if XZ is equal to 10 .
2
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If AB is equal to 10 ft, AC is equal to 14 ft, and BC is equal to 20 ft, what is RS ?

A
24 ft
B
14 ft
C
10 ft
D
20 ft
3

What is the missing reason in the proof? Statements Reasons 1. angle EGF is congruent to angle HGK 1. vert. angle cap s are is congruent to 2. line segment KH is parallel to line segment EF 2. given 3. angle cap f is congruent to angle cap k 3. alt. int. angle cap s are is congruent to 4. cap g is the midpoint of line segment KF 4. given 5. line segment FG is congruent to line segment KG 5. def. of midpt. 6. triangle FEG is congruent to triangle KHG 6. ? 7. line segment HG is congruent to line segment EG 7. CPCTC

A
SAS
B
ASA
C
HL
D
AAS
4

Two rigid transformations are used to map triangle cap A cap b cap c to triangle cap q cap r cap s The first is a translation of vertex cap b to vertex cap r What is the second transformation?

A
a reflection across the line containing line segment cap c cap b
B
a reflection across the line containing line segment cap A cap b
C
a rotation about point cap c
D
a rotation about point cap b
5

How can a translation and a reflection be used to map triangle HJK to triangle LMN ?

A
Translate cap k to cap n and reflect across the line containing line segment JK .
B
Translate cap k to cap n and reflect across the line containing line segment HJ .
C
Translate cap h to cap l and reflect across the line containing line segment JK .
D
Translate cap k to cap l and reflect across the line containing line segment HJ .
6

If AB is equal to 6 units, BC is equal to 5 units, CD is equal to 8 units, and AD is equal to 10 units, what is LO ?

A
5 units
B
6 units
C
8 units
D
10 units
7

What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem?

A
angle cap l cap o cap A is congruent to angle cap l cap m cap A
B
line segment cap l cap o is congruent to line segment cap l cap m
C
angle cap l cap A cap o is congruent to angle cap l cap A cap m
D
line segment cap o cap A is congruent to line segment cap m cap A
8

Is there a series of rigid transformations that could map triangle QRS to triangle ABC ? If so, which transformations could be used?

A
Yes, triangle QRS can be translated so that cap q is mapped to cap A and then reflected across the line containing line segment QS .
B
Yes, triangle QRS can be translated so that cap r is mapped to cap b and then rotated so that cap s is mapped to cap c .
C
No, triangle QRS and triangle ABC are not congruent.
D
No, triangle QRS and triangle ABC are congruent but triangle QRS cannot be mapped to triangle ABC using a series rigid transformations.
9

In the diagram, angle cap j is congruent to angle cap m and line segment JL is congruent to line segment MR What additional information is needed to show triangle JKL is congruent to triangle MNR by SAS?

A
line segment KL is congruent to line segment NR
B
line segment JK is congruent to line segment MN
C
angle cap k is congruent to angle cap n
D
angle liters is congruent to angle cap r
10

What is the missing reason in the proof? Statements Reasons 1. line segment SP is congruent to line segment SR 1. given 2. line segment ST perpendicular to line segment PR 2. converse of the perpendicular bisector theorem 3. line segment PT is congruent to line segment RT 3. ? 4. line segment QT perpendicular to line segment PR 4. line segment ST and line segment QT name the same line. 5. line segment QP is congruent to line segment QR 5. perpendicular bisector theorem 6. triangle QPT is congruent to triangle QRT 6. HL theorem

A
substitution property
B
definition of congruence
C
definition of perpendicular bisector
D
reflexive property
11

Is triangle cap m cap n cap l is congruent to triangle cap q cap n cap l ? Why or why not?

A
No, angle cap m is not congruent to angle cap n cap l cap q .
B
Yes, they are congruent by either ASA or AAS.
C
No, there are no congruent sides.
D
Yes, they are both right triangles.
12

Which rigid transformation(s) can map triangle MNP onto triangle TSR ?

A
reflection only
B
translation, then rotation
C
translation, then reflection
D
rotation only
13

What is the missing reason in the proof?

A
the third angle theorem
B
ASA
C
AAS
D
the reflexive property
14

Triangle DEF is congruent to triangle GHJ by the SSS theorem. Which rigid transformation is required to map triangle DEF onto triangle GHJ ?

A
rotation
B
reflection
C
dilation
D
translation
15

Which relationship in the diagram is true?

A
triangle SNQ is congruent to triangle SNM by SSS
B
triangle RMS is congruent to triangle RQS by AAS
C
triangle QNR is congruent to triangle MNR by HL
D
triangle MNR is congruent to triangle MNS by ASA
16

If line segment CB bisects angle ACD , what additional information could be used to prove triangle ABC is congruent to triangle DBC using SAS? Choose three correct answers.

A
triangle ACD is isosceles with base line segment AD
B
triangle ABD is isosceles with base line segment AD
C
CD is equal to 52 cm
D
AB is equal to 29 cm
E
m angle ABC is equal to 125 degrees and line segment AB is congruent to line segment DB
17

In triangle XYZ , m angle cap x is equal to 90 degrees and m angle cap y is equal to 30 degrees In triangle TUV , m angle cap u is equal to 30 degrees and m angle cap v is equal to 60 degrees Which is true about the two triangles?

A
No congruency statement can be made because the side lengths are unknown.
B
triangle XYZ is congruent to triangle TUV
C
No congruency statement can be made because only two angles in each triangle are known.
D
triangle XYZ is congruent to triangle VUT
18

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?

A
AAS
B
HL
C
SSS
D
SAS
19

Three quadrilaterals exist such that GHJK≅ASDF and GHJK≅VBNM. If line segment MV measures 3 cm, which other segment must measure 3 cm?

A
line segment AF
B
line segment KJ
C
line segment FD
D
line segment GJ
20

Which pair of triangles can be proven congruent by SAS?

A
Image with description Two triangles share a diagonal side. The shared diagonal has triple tick marks. One pair of outer sides has matching single tick marks, and another pair of outer sides has matching double tick marks.
B
Image with description Two triangles share one side. The shared side has a tick mark. A pair of angles at one endpoint of the shared side have matching single arc marks, and a pair of angles at the other endpoint have matching double arc marks.
C
Image with description Two separate triangles are shown. In the left triangle, the bottom side has a single tick mark, the right slanted side has double tick marks, and the angle at the left endpoint of the bottom side has an arc mark. In the right triangle, the left vertical side has a single tick mark, the upper slanted side has double tick marks, and the angle at the lower endpoint of the vertical side has an arc mark.
D
Image with description A triangle is divided into two right triangles by a segment from the top vertex to the base. The shared segment has double tick marks, the two base segments have matching single tick marks, and right-angle markers are shown where the shared segment meets the base.

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