AnswersGeometryRelationships of Triangles: Congruence

Practice Test Answers

20 verified answers
1
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Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof? Given: angle cap b is congruent to angle cap n ; line segment cap b cap c is congruent to line segment cap n cap m ; angle cap c is right; angle cap m is right Prove: triangle cap A cap b cap c is congruent to triangle cap q cap n cap m

A
angle cap A is congruent to angle cap q because of the third angle theorem.
B
line segment cap b cap c is congruent to line segment cap n cap m because it is given.
C
angle cap c is congruent to angle cap m because right angles are congruent.
D
line segment cap A cap b is congruent to line segment cap q cap n because they are both opposite a right angle.
2
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Which must be true?

A
Point cap A is not necessarily the center of the circle that passes through points cap e , cap f , and cap g or the center of the circle that passes through points cap x , cap y , and cap z .
B
Point cap A is the center of the circle that passes through points cap e , cap f , and cap g and the center of the circle that passes through points cap x , cap y , and cap z .
C
Point cap A is the center of the circle that passes through points cap e , cap f , and cap g but is not the center of the circle that passes through points cap x , cap y , and cap z .
D
Point cap A is the center of the circle that passes through points cap x , cap y , and cap z but is not the center of the circle that passes through points cap e , cap f , and cap g .
3

Which rigid transformation would map triangle ABC to triangle ABF ?

A
a rotation about point cap A
B
a rotation about point cap b
C
a reflection across the line containing line segment CB
D
a reflection across the line containing line segment BA
4

In triangle ABC , the segments drawn from the vertices intersect at point cap g Segment FG measures 6 cm, and segment FC measures 18 cm. Which best explains whether point cap g can be the centroid?

A
Point cap g cannot be the centroid because ratio of 18 to 6 does not equal ratio of 2 to 1 .
B
Point cap g can be the centroid because ratio of 12 to 6 equals ratio of 2 to 1 .
C
Point cap g cannot be the centroid because FG should be longer than CG .
D
Point cap g can be the centroid because FC is longer than FG .
5

Which must be true?

A
line segment TA is congruent to line segment TB
B
line segment AZ is congruent to line segment BZ
C
angle BTZ is congruent to angle BUZ
D
angle TZA is congruent to angle TZB
6

Which pair of angles is supplementary?

A
angle PXQ and angle RXS
B
angle WZX and angle XYZ
C
angle YZX and angle UZT
D
angle RXZ and angle YXZ
7

In the diagram, which must be true for point cap p to be the centroid of the triangle?

A
JL is equal to LK is equal to KJ
B
line segment LN perpendicular to line segment JK , line segment JO perpendicular to line segment LK , and line segment JL perpendicular to line segment MK .
C
JM is equal to ML , LO is equal to OK , and KN is equal to NJ .
D
line segment LN is a perpendicular bisector of line segment JK , line segment JO is a perpendicular bisector of line segment LK , and line segment MK is a perpendicular bisector of line segment JL .
8

First, translate ____________________. Next, rotate triangle ABC about cap b to align the sides and angles.

A
vertex cap b to vertex cap z
B
vertex cap b to vertex cap y
C
vertex cap A to vertex cap z
D
vertex cap A to vertex cap y
9

Triangle RST is rotated 180 degrees about the origin, and then translated up 3 units. Which congruency statement describes the figures?

A
triangle RST is congruent to triangle ACB
B
triangle RST is congruent to triangle ABC
C
triangle RST is congruent to triangle BAC
D
triangle RST is congruent to triangle BCA
10

The congruence theorem that can be used to prove triangle BAE is congruent to triangle CAD is

A
HL.
B
ASA.
C
SAS.
D
SSS.
11

Could triangle ABC be congruent to triangle ADC by SSS? Explain.

A
No, because line segment AB is not congruent to line segment AC .
B
Yes, but only if line segment AB is congruent to line segment DC .
C
Yes, but only if line segment BC is congruent to line segment DC .
D
No, because line segment AB is congruent to line segment DA .
12

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

A
angle cap j cap k cap g is congruent to angle cap h cap f cap g because vertical angles are congruent.
B
angle cap h cap f cap g is congruent to angle cap k cap j cap g because alternate interior angles are congruent.
C
angle cap f cap g cap h is congruent to angle cap k cap g cap j because vertical angles are congruent.
D
angle cap f cap h cap g is congruent to angle cap j cap k cap g because right angles are congruent.
13

Which congruence theorem can be used to prove triangle BDA is congruent to triangle DBC ?

A
AAS
B
SAS
C
HL
D
SSS
14

Which new angle is created by extending one side of a triangle?

A
a remote interior angle
B
a complementary angle
C
an adjacent interior angle
D
an exterior angle
15

Which best explains whether or not triangles RST and ACB are congruent?

A
The figures are congruent. triangle RST can be mapped to triangle ACB by a reflection over the x -axis and a translation 2 units to the left.
B
The figures are not congruent. Point cap r corresponds to point cap A , but cap s corresponds to cap b and cap t corresponds to cap c .
C
The figures are congruent. triangle RST can be mapped to triangle ACB by a reflection over the y -axis and a translation 2 units down.
D
The figures are not congruent. Point cap r does not correspond with point cap A .
16

Which diagram shows possible angle measures of a triangle?

A
Image with description A triangle has angles labeled 35 degrees at the lower-left vertex, 120 degrees at the top vertex, and 35 degrees at the lower-right vertex.
B
Image with description A triangle has angles labeled 30 degrees at the lower-left vertex, 120 degrees at the top vertex, and 20 degrees at the lower-right vertex.
C
Image with description A triangle has angles labeled 32 degrees at the lower-left vertex, 115 degrees at the top vertex, and 33 degrees at the lower-right vertex.
D
Image with description A triangle has angles labeled 35 degrees at the lower-left vertex, 115 degrees at the top vertex, and 25 degrees at the lower-right vertex.
17

Which pair of triangles can be proven congruent by the HL theorem?

A
Image with description Two separate right triangles are shown. Each triangle has a right-angle marker, and the side opposite the right angle has a single tick mark. No other sides are marked.
B
Image with description Two separate triangles are shown. In the left triangle, one side has a single tick mark, the opposite side has double tick marks, and the angle between the single-tick side and an unmarked side has an arc mark. In the right triangle, one side has a single tick mark, the opposite side has double tick marks, and the angle between the single-tick side and an unmarked side has an arc mark. No right-angle markers are shown.
C
Image with description Two separate triangles are shown with no right-angle markers. In the upper triangle, the left side has a single tick mark, the lower-right side has double tick marks, and the upper-right side has triple tick marks. In the lower triangle, the bottom side has a single tick mark, the right slanted side has double tick marks, and the left side has triple tick marks.
D
Image with description Two separate right triangles are shown. In each triangle, the side opposite the right angle has double tick marks, and one side adjacent to the right angle has a single tick mark.
18

Triangle ABC has the angle measures shown. m angle cap A is equal to 2 x degrees m angle cap b is equal to 5 x degrees m angle cap c is equal to 11 x degrees Which statement is true about the angles?

A
m angle cap A plus m angle cap c is equal to 120 degrees
B
m angle cap A is equal to 20 degrees
C
m angle cap b is equal to 60 degrees
D
angle cap A and angle cap b are complementary
19

Which type of triangle will always have a perpendicular bisector that is also an angle bisector?

A
scalene
B
right
C
equilateral
D
obtuse
20

The base angle of an isosceles triangle measures 54 degrees What is the measure of its vertex angle?

A
36 degrees
B
72 degrees
C
27 degrees
D
54 degrees

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