Geometry Test – Unit 4a
Triangle Relationships
☺Name: ___________________☺
Date: ___________ Pd: ____
Definitions (1-4)
1) Equilateral triangle
2)
Base angles of an isosceles triangle
3)
Hypotenuse Leg Theorem (HL)
4)
Exterior Angle Theorem
5)
Draw and label all parts of a(n): (mark all congruent sides and angles)
a) right triangle.
b) isosceles triangle.
6)
Which, if any, congruence theorem or postulate would prove the triangles are congruent?
F
C
A
D
B
E
Write a congruence statement if possible: ___________________________
7) Which, if any, congruence theorem or postulate would prove the triangles are congruent?
D
A
C
B
Write a congruence statement if possible: ___________________________
Unit 4a: TEST
Triangle Relationships 2011
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8)
Find the value of x.
x
55
9)
Find the value of x.
(2x - 30)
2x 
50
10)
Find the value of x.
(3x - 3)
x
65
11)
In the figure below, ABCDE  LMNOP . Which angle of LMNOP corresponds to DEA ?
B
C
N
O
M
A
D
P
E
Unit 4a: TEST
Triangle Relationships 2011
L
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12)
Given that ABC  XYZ , BC  2 3x  10  and YZ   x  15  , find the value of x.
HINT – Draw & label the picture!
13)
Given that GHI  JKL , m H  (5x  28), m I  (3x  41), and m J  2x  11   , find
mK .
14)
HINT – Draw & label the picture!
Fill in the blank:
CPCTC can only be used ______ proving two triangles are __________.
State the reason for the statement in Step 4.
Given:
Prove:
AE and BD bisect each
other at C
B
DE  BA
E
C
A
Statements
1) AE and BD bisect
each other at C
2) AC  CE
Reasons
1) Given
3) BC  CD
4) ACB  DCE
5) ABC  EDC
2) Def. of bisect
3) Def. of bisect
4) ______________________
5) SAS
6) DE  BA
6) CPCTC
Unit 4a: TEST
D
Triangle Relationships 2011
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15)
Write a two-column proof.
Given:
L
K
KPL is equilateral,
J
JP  MP ,
JPK  MPL
M
Prove:
JPK  MPL
P
Semester Exam Review
16. Which is a valid classification for a triangle?
A. equilateral scalene
B. isosceles scalene
C. obtuse isosceles
D. right acute
17. In the diagram, ABCDE  RSTUV .
A
E
D
B
U
T
C
V
S
R
Which side of ABCDE corresponds to VR ?
A. CB
B. DC
C. EA
D. ED
Unit 4a: TEST
Triangle Relationships 2011
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18. Use the triangles.
Which congruence postulate or theorem proves these two triangles are congruent?
A. angle-angle-angle (AAA)
B. angle-side-angle (ASA)
C. side-angle-side (SAS)
D. side-side-side (SSS)
19. In the diagram, AD  CD and B is the midpoint of AC .
D
A
B
C
Which congruence postulates or theorems would prove these two triangles are congruent?
I. side-side-angle (SSA)
II. side-angle-side (SAS)
III. side-side-side (SSS)
A. II only
B. III only
C. I and II only
D. II and III only
Unit 4a: TEST
Triangle Relationships 2011
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20. Given that RST  XYZ , mR   3b  20   , mY  40 , and mZ  45 , what is the value of b?
A. 21
2
3
B. 25
C. 38
1
3
D. 95
21. Given that  PQR   JKL , JK  3 x  9 , KL  2 x , LJ  6 x , and PQ  5 x  3 ; what is the value of
x?
A. –1
B. 1
C. 3
D. 6
22. The statements for a proof are given below.
Given: Parallelogram ABCD
AXB  CYD
Prove:
AX  CY
X
B
A
C
D
Y
Proof:
STATEMENTS
REASONS
1. Parallelogram ABCD
AXB  CYD
1.
2. B  D
2.
3. AB  CD
3.
4. ABX  CDY
4.
5. AX  CY
5.
Unit 4a: TEST
Triangle Relationships 2011
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What reason makes the statement in Step 4 true?
A. angle-angle-side (AAS)
B. angle-side-angle (ASA)
C. side-angle-side (SAS)
D. side-side-side (SSS)
23. The statements for a proof are given below.
AB  FD
Given:
A  D
F  B
BC  EF
Prove:
E
B
D
A
C
F
Proof:
STATEMENTS
REASONS
1. AB  FD
1.
2. A  D
2.
3. F  B
3.
4. ABC  DFE
4.
5. BC  EF
5.
What reason makes the statement in Step 5 true?
A. corresponding parts of congruent triangles are congruent. (CPCTC)
B. angle-side-angle (ASA)
C. side-angle-angle (SAA)
D. given
Unit 4a: TEST
Triangle Relationships 2011
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24. Given that DEF  LMN , mD   5 x  10   , mL   4 x  10   , and DF  3  x  5  ; what is
LN?
A. 15
B. 20
C. 65
D. 75
25. In the isosceles triangle, mH  130 .
H
130°
F
G
What is the measure of G ?
A. 25°
B. 35°
C. 50°
D. 65°
SAT Review
26.
If XYX is equilateral, what is the value of r  s  t  u ?
Unit 4a: TEST
Grid In
Triangle Relationships 2011
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27. (LTMR) In the diagram, m n and t is a transversal.
m
n
t
134°
 2 x  10  
What is the value of x?
28. (LTMR) What is the slope of any line perpendicular to y  .5x  3 .
Unit 4a: TEST
Triangle Relationships 2011
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