AnswersPMHS Geometry Q2Using Triangle Congruence Theorems

Using Triangle Congruence Theorems — Unit test Answers

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Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Question illustration
A
Yes, they are congruent by either ASA or AAS.
B
Yes, they are both right triangles.
C
No, M is not congruent to NLQ.
Option C
D
No, there are no congruent sides.
2
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Point Z is the incenter of ΔSRT.

Question illustration
A
24°
B
31°
C
35°
D
62°
3

Consider triangle WXY.

Question illustration
A
Angle W is greater than angle Y.
B
Angle Y is the largest angle.
C
Angle X is smaller than angle W.
D
Angle W is the smallest angle.
4

Which must be true? Select two options.

A
Point H is the center of the circle that passes through points D, E, and F.
B
Point H is the center of the circle that passes through points L, M, and N.
C
Line segment H E is-congruent-to line segment H D
Option C
D
Line segment L H is-congruent-to line segment N H
Option D
E
Line segment F L is-congruent-to line segment F N
Option E
5

The proof that ΔQPT ≅ ΔQRT is shown.Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT

Question illustration
A
definition of perpendicular bisector
B
definition of congruence
C
reflexive property
D
substitution property
6

The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

Question illustration
A
the reflexive property
B
ASA
C
AAS
D
the third angle theorem
7

Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.

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

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Question illustration
A
Yes, if JL ≅ XZ.
B
Yes, if XZ = 10.
C
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
D
No, because the leg of one triangle is equal in length to the leg of the other triangle.
9

Triangles H J K and L M N are shown. The triangles have identical side lengths and angle measures. Triangle H J K is slightly lower and to the left of triangle L M N. Triangle H J K is reflected to form triangle L M N.

Question illustration
A
Translate K to N and reflect across the line containing HJ.
B
Translate K to N and reflect across the line containing JK.
C
Translate H to L and reflect across the line containing JK.
D
Translate K to L and reflect across the line containing HJ.
10

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

A
AF
B
KJ
C
FD
D
GJ
11

Nigel and Mia are searching for a treasure chest under water. The straight line distance between them is 100 meters.

Question illustration
A
Nigel is closer because his distance to the chest is opposite the larger angle.
B
Mia is closer because her distance to the chest is opposite the smaller angle.
C
Nigel is closer because his distance from the chest is 100 meters.
D
Mia is closer because her distance from the chest is 100 meters.
12

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

A
ΔXYZ ≅ ΔTUV
B
ΔXYZ ≅ ΔVUT
C
No congruency statement can be made because only two angles in each triangle are known.
D
No congruency statement can be made because the side lengths are unknown.
13

Triangle XYZ is isosceles. Angle Y measures a°.

Question illustration
A
2a
B
StartFraction a Over 2 EndFraction
Option B
C
90 a
Option C
D
180 2a
Option D
14

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees.

Question illustration
A
m∠ABC = 15°
B
m∠ABC = 45°
C
m∠ABC = 60°
D
m∠ABC = 75°
15

Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3.

Question illustration
A
1 unit
B
2 units
C
4 units
D
6 units
16

Triangle KNM is shown.

Question illustration
A
KN = NM
B
KN + NM = KM
C
KM = 2(NM)
D
KN = KM
Option D
17

Which pair of triangles can be proven congruent by SAS?

A
2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.
Option A
B
2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.
Option B
C
2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.
Option C
D
2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.
Option D
18

The proof that HG ≅ EG is shown.Given: G is the midpoint of KFKH ∥ EFProve: HG ≅ EGWhat is the missing reason in the proof?StatementReason1. ∠EGF ≅ ∠HGK1. vert. ∠s are ≅2. KH ∥ EF2. given3. ∠F ≅ ∠K3. alt. int. ∠s are ≅4. G is the midpoint of KF4. given5. FG ≅ KG5. def. of midpt.6. △FEG ≅ △KHG6. ?7. HG ≅ EG7. CPCTC

Question illustration
A
SAS
B
ASA
C
AAS
D
HL
19

If triangle RST is an acute triangle, then m∠S must be

A
less than 90°.
B
equal to 90°.
C
equal to 100°.
D
greater than 90° and less than 180°.
20

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

A
m∠A = 15° and m∠C = 35°
B
m∠A + m∠B = 155°
C
m∠A + m∠C = 60°
D
m∠A = 20° and m∠C = 30°

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