AnswersGeometryRelationships of Triangles: Congruence

Relationships of Triangles: Congruence — Test Answers

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Which must be true? Choose two correct answers.

A
line segment LH is congruent to line segment NH
B
Point cap h is the center of the circle that passes through points cap d , cap e , and cap f .
C
line segment FL is congruent to line segment FN
D
line segment HE is congruent to line segment HD
E
Point cap h is the center of the circle that passes through points cap l , cap m , and cap n .
3

Which angle is an adjacent interior angle to angle JKM ?

A
angle JKL
B
angle KLM
C
angle LMK
D
angle MKL
4

Which relationship in the diagram is true?

A
triangle RMS is congruent to triangle RQS by AAS
B
triangle SNQ is congruent to triangle SNM by SSS
C
triangle MNR is congruent to triangle MNS by ASA
D
triangle QNR is congruent to triangle MNR by HL
5

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
7

In triangle TRS , VZ is equal to 6 inches. What is RZ ?

A
6 inches
B
18 inches
C
12 inches
D
3 inches
8

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

A
No, there are no congruent sides.
B
Yes, they are congruent by either ASA or AAS.
C
No, angle cap m is not congruent to angle cap n cap l cap q .
D
Yes, they are both right triangles.
9

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

A
line segment cap o cap A is congruent to line segment 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
angle cap l cap o cap A is congruent to angle cap l cap m cap A
11

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

A
equal to 100 degrees .
B
greater than 90 degrees and less than 180 degrees .
C
less than 90 degrees .
D
equal to 90 degrees .
12

Which must be true?

A
line segment NC is congruent to line segment BZ
B
angle ZBM is congruent to angle ZCM
C
angle BMZ is congruent to angle CMZ
D
line segment AN is congruent to line segment LB
13

What is true about the sides of KNM ?

A
KN plus NM is equal to KM
B
KM is equal to 2 times NM
C
KN is equal to 1 half KM
D
KN is equal to NM
14

What is the missing reason in the proof?

A
AAS
B
ASA
C
the third angle theorem
D
the reflexive property
15

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 h to cap l and reflect across the line containing line segment JK .
C
Translate cap k to cap l and reflect across the line containing line segment HJ .
D
Translate cap k to cap n and reflect across the line containing line segment HJ .
16

What is m angle ABC ?

A
m angle ABC is equal to 45 degrees
B
m angle ABC is equal to 60 degrees
C
m angle ABC is equal to 15 degrees
D
m angle ABC is equal to 75 degrees
17

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

A
line segment BE , line segment CF , and line segment AG are angle bisectors.
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 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 .
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 .
19

What is the length of XB ?

A
4 point 2 cm
B
4 point 8 cm
C
4 point 6 cm
D
5 point 3 cm

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