AnswersGeometryRelationships of Triangles: Congruence

Relationships of Triangles: Congruence — Test Answers

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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 r is mapped to cap b and then rotated so that cap s is mapped to cap c .
B
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 .
C
No, triangle QRS and triangle ABC are congruent but triangle QRS cannot be mapped to triangle ABC using a series rigid transformations.
D
No, triangle QRS and triangle ABC are not congruent.
4

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

A
Yes, they are both right triangles.
B
Yes, they are congruent by either ASA or AAS.
C
No, there are no congruent sides.
D
No, angle cap m is not congruent to angle cap n cap l cap q .
6

What is the length of segment NS ?

A
1 unit
B
6 units
C
4 units
D
2 units
7

In the diagram, which must be true for point cap d to be an orthocenter?

A
line segment BE is a perpendicular bisector of line segment AC , line segment CF is a perpendicular bisector of line segment AB , and line segment AG is a perpendicular bisector of line segment BC .
B
line segment BE bisects line segment AC , line segment CF bisects line segment AB , and line segment AG bisects line segment BC .
C
line segment BE , line segment CF , and line segment AG are angle bisectors.
D
line segment BE perpendicular to line segment AC , line segment AG perpendicular to line segment BC , and line segment CF perpendicular to line segment AB .
8

What expression represents the measure of angle cap x ?

A
90 minus A
B
180 minus 2 A
C
A over 2
D
2 A
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 JK is congruent to line segment MN
B
line segment KL is congruent to line segment NR
C
angle liters is congruent to angle cap r
D
angle cap k is congruent to angle cap n
10

Based on the diagram, which expresses all possible lengths of segment AB ?

A
AB is equal to 25
B
27 is less than AB comma AB is less than 81
C
AB is equal to 85
D
AB is less than 27 or AB is greater than 81
11

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

A
line segment cap l cap o is congruent to line segment cap l cap m
B
angle cap l cap A cap o is congruent to angle cap l cap A cap m
C
line segment cap o cap A is congruent to line segment cap m cap A
D
angle cap l cap o cap A is congruent to angle cap l cap m cap A
12

If triangle RST is an acute triangle, then m angle cap s must be

A
equal to 100 degrees .
B
less than 90 degrees .
C
greater than 90 degrees and less than 180 degrees .
D
equal to 90 degrees .
13

If triangle ABC has a 130 degrees angle at vertex cap b , which statement must be true?

A
m angle cap A is equal to 20 degrees and m angle cap c is equal to 20 degrees
B
m angle cap A is equal to 15 degrees and m angle cap c is equal to 35 degrees
C
m angle cap A plus m angle cap b is equal to 180 degrees
D
m angle cap A plus m angle cap c is equal to 50 degrees
14

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
triangle XYZ is congruent to triangle VUT
B
triangle XYZ is congruent to triangle TUV
C
No congruency statement can be made because the side lengths are unknown.
D
No congruency statement can be made because only two angles in each triangle are known.
15

What is the missing reason in the proof?

A
the third angle theorem
B
the reflexive property
C
ASA
D
AAS
18

Which statements regarding the diagram of triangle EBC are true? Choose three correct answers.

A
angle BEC is a remote interior angle to exterior angle BCF .
B
angle BEC is an exterior angle.
C
angle BCF and angle DEC are supplementary angles.
D
angle ABE and angle EBC are supplementary angles.
E
angle DEC is an exterior angle.
19

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
Yes, if XZ is equal to 10 .
C
No, because the leg of one triangle is equal in length to the leg of the other triangle.
D
Yes, if line segment JL is congruent to line segment XZ .
20

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

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

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