AnswersRecovery Content Sec Math 1 - Quarter 4 - 202627Triangle Congruence: SAS

Triangle Congruence: SAS — Unit test Answers

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21
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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
22
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Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

Question illustration
A
∠JKL
B
∠MKL
C
∠KLM
D
∠LMK
23

Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS

Question illustration
A
ΔMNR ≅ ΔMNS by ASA
B
ΔRMS ≅ ΔRQS by AAS
C
ΔSNQ ≅ ΔSNM by SSS
D
ΔQNR ≅ ΔMNR by HL
24

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.
25

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.
26

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
reflection only
B
rotation only
C
translation, then reflection
D
translation, then rotation
27

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
28

Triangles D E F and G H J are congruent. Triangle D E F is shifted down and to the right to form triangle G H J.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
29

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
30

Point Z is the incenter of ΔSRT.

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

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
32

Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?

A
AAS
B
SSS
C
SAS
D
HL
33

Point X is the circumcenter of ΔABC.What is the length of XB?

Question illustration
A
4.2 cm
B
4.6 cm
C
4.8 cm
D
5.3 cm
34

Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

Question illustration
A
a reflection across the line containing AB
B
a rotation about point B
C
a reflection across the line containing CB
D
a rotation about point C
35

Quadrilateral L M N O is reflected over a line to form quadrilateral C D A B.

Question illustration
A
AB
B
AD
C
CB
D
DC
36

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°
37

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.

Question illustration
A
9 units
B
12 units
C
15 units
D
18 units
38

Quadrilateral JKLM was dilated according to the ruleDO,(x,y) to create the image quadrilateral J'K'L'M', which is shown on the graph.

Question illustration
A
(0, -4)
B
(0, -1)
C
(0, 0)
D
(0, 4)
39

Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.

Question illustration
A
because both triangles appear to be equilateral
B
because∠MNL and ∠ONP are congruent angles
C
because one pair of congruent corresponding angles is sufficient to determine similar triangles
D
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
40

Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.

Question illustration
A
3
B
8
C
10
D
11

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