AnswersPMHS Geometry Q2Using Triangle Congruence Theorems

Using Triangle Congruence Theorems — Unit test Answers

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Triangle A B C is shown. Lines are drawn from each point to to the opposite side and intersect at point G. Line segments A D, B E, and C F are created.

Question illustration
A
Point G cannot be the centroid because 18:6 does not equal 2:1.
B
Point G cannot be the centroid because FG should be longer than CG.
C
Point G can be the centroid because 12:6 equals 2:1.
D
Point G can be the centroid because FC is longer than FG.
2
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Triangle B C D is shown. Line D B extends through point A to form exterior angle A B C. Angle B D C is 67 degrees and Angle C D B is 60 degrees.

Question illustration
A
m∠ABC = 60°
B
m∠ABC = 67°
C
m∠ABC = 120°
D
m∠ABC = 127°
3

In the triangles, HG = MP and GK = PN.

Question illustration
A
mG > mP
Option A
B
mP > mG
Option B
C
HK = MN
D
HG = PN
4

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?

Q
QS = 13
5
5 < QS < 8
Q
QS > 13
3
3 < QS < 13
5

[Figure may not be drawn to scale]

Question illustration
A
25 units
B
50 units
C
100 units
D
150 units
6

Consider the triangle.

Question illustration
A
mA = 95°, mB = 53°, mC = 32°
Option A
B
mA = 32°, mB = 53°, mC = 95°
Option B
C
mA = 43°, mB = 32°, mC = 95°
Option C
D
mA = 53°, mB = 95°, mC = 32°
Option D
7

[Figure may not be drawn to scale]

Question illustration
A
12 mm
B
24 mm
C
36 mm
D
48 mm
8

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

A
right
B
scalene
C
obtuse
D
equilateral
9

Consider the triangle shown.

Question illustration
A
Line segment P Q, line segment R Q, line segment R P
Option A
B
Line segment R Q, Line segment P Q, line segment P Q
Option B
C
Line segment R Q, line segment R P, line segment P Q
Option C
D
Line segment R P, line segment P Q, line segment R Q
Option D
10

Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circular water bowl. It should go all the way to the edges of the table as shown.

Question illustration
A
He should find the midpoint of each edge of the table.
B
He should bisect each of the angles at the vertices of the triangular table top.
C
He should draw perpendicular lines through any point along the edges of the table.
D
He should draw perpendicular line segments from each corner to the opposite edge of the table.
11

Lines P S and W T are horizontal and parallel. Lines V R and Q R are diagonal and intersect lines P S and W T to form triangle X Y Z.

Question illustration
A
∠RXZ and ∠YXZ
B
∠PXQ and ∠RXS
C
∠YZX and ∠UZT
D
∠WZX and ∠XYZ
12

Triangle ABC has the angle measures shown.

Question illustration
A
Measure of angle A = 20 degrees
Option A
B
Measure of angle B = 60 degrees
Option B
C
are complementary
Option C
D
Measure of angle A + measure of angle C = 120 degrees
Option D
13

In the triangles, and .

Question illustration
A
mC = mS
Option A
B
mC < mS
Option B
C
mC > mS
Option C
D
mC ≥ mS
Option D
14

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees.

Question illustration
A
h = 1.5
B
h = 9
C
h = 10
D
h = 13.5
15

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

2
27°
3
36°
5
54°
7
72°
16

Point Z is equidistant from the vertices of ΔTUV.

Question illustration
A
Line segment T A is-congruent-to line segment T B
Option A
B
Line segment A Z is-congruent-to line segment B Z
Option B
C
BTZ BUZ
Option C
D
TZA TZB
Option D
17

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.HLSASSSSASAAAS

Question illustration
A
HL
B
SAS
C
SSS
D
ASA
E
AAS
18

[Figure may not be drawn to scale]

Question illustration
A
12 mm
B
24 mm
C
36 mm
D
48 mm
19

In the triangles, and .

Question illustration
A
mC = mS
Option A
B
mC < mS
Option B
C
mC > mS
Option C
D
mC ≥ mS
Option D
20

is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and .

Question illustration
A
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
B
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
C
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
D
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z.

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