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Geometry
Unit 4 Review
Revised Summer 08
Show all work on a separate sheet of work paper. Remember to follow the criteria
for credit.
Competency 1: Triangles and Angles
Competency 2: Identify congruence
1. Sketch a triangle to fit the
description. If not possible, write Not
Possible. Sketch a right, isosceles
triangle.
For questions 7 – 11, decide if there is a
0congruence postulate you can use to
prove that the given triangles are
congruent. If so, write the congruence
statement and identify the postulate. If
not, write Not Possible.
2. A triangle with no sides congruent is
a(n) _____________ triangle.
7.
A
D
B
3. A triangle with a 125 angle is a(n)
_____________ triangle.
C
8.
4. Using the given information in the
drawing below, find the values of
x and y.
E
R
F
O
S
N
T
M
x°
100°
y°
9.
5. Using the given information in the
drawing below, find the values of
x and y.
P
A
2"
2"
2"
Q
2"
R
B
30°
x°
y°
A
10.
6. Find the measures of the angles of
this triangle.
D
C
(3x – 16)°
(x + 11)°
E
B
x°
M
11.
6 cm
6 cm
N
Page 1 of 4
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O
P
C
Geometry
Unit 4 Review
Competency 3: Congruence of
triangles
16. a) Copy the given figure and mark
any parts that are equal in measure
For questions 12 and 13, identify the
congruent triangles from the given
drawings, and state how you know that
they are congruent.
b) Identify how you would prove the
triangles congruent.
Given: SQ and PR bisect each
other.
12.
N
Revised Summer 08
R
O
R
S
P
M
T
13.
P
X
W
Y
Z
Competency 4: Using congruence in
applications
For questions 14 and 15, state one
additional fact that is needed for the pair
of triangles to be congruent. State why
they would be congruent
14.
Q
B
D
For the two partial proofs below, supply
the missing statements or reasons.
Proof #1
Given: AB  DE , AB  DE 
Prove: ABC  DEC
C
E
A


C
A
E
F
B
15.
V
X
Y
Z
Page 2 of 4
W
Statement
1. AB  DE
AB  DE
2. A  D
B  E
3. ABCDEC
© Mastery Mathematics
Reason
1. Given
17.
18.
D
Geometry
Unit 4 Review
Proof #2
Revised Summer 08
23. Use the information provided in the
drawing to find x and y.
Given: XY  XZ , XWYZ
Prove: 1  2
x°
X
1 2
40°
y°
Y
3 4
W
24. Use the information provided in the
drawing to find x and y.
Z
Statement
1. XY  XZ ,
XWYZ
19.
Reason
1. Given
x° 120°
2. If 2 lines are
, they form
right angles
3. Reflexive
Property
4.Definition of
a right 
5. HL Theorem
21.
20.
4. XWY&XWZ
are right s
5. XWYXWZ
6. 12
y°
30°
25. Use the information provided in the
drawing to find x.
56'
(8x)'
Competency 5: Isosceles, Equilateral
Triangles
26. Use the information provided in the
drawing to find x and y.
22. Use the information provided in the
drawing to find x and y.
y°
50°
Page 3 of 4
y°
70°
x°
x°
© Mastery Mathematics
Geometry
Unit 4 Review
Revised Summer 08
Competency 6: D.P.- Multiple Choice
27. In the diagram below, ab. Find
m  1 and m 2, if m 1 = 3x + 60 and
m 2 = 6x – 30.
[A] 3  
t
a
30. Write the equation of a line that has
a y-intercept of –3 and is perpendicular
2
to the graph of y  x .
3
[C] y 
2
x3
3
1
[B] y  
b
2
[A] m  1 = 30  , m 2 = 150 
[B] m  1 = 30  , m 2 = 60 
[C] m  1 = 150  , m 2 = 150 
[D] m  1 = 150  , m 2 = 30 
28. Find the slope of the line parallel to
the graph of 3x + 2y = 8.
3
[A] 
2
2
[B] 
3
3
[C]
2
2
[D]
3

29. Using the drawing below name two
lines that are skew to DG .
J
D
I
E
3
x3
2
[D] y  3x 
2
3
31. Which of the following arguments is
INVALID? Justify your answer in
the space provided.
[A]
If two angles form a linear pair, then
they are supplementary.
 A and  B are supplementary.
So,  A and  B form a linear pair.
[B]
If the sum of the measure of two
angles is 90  , then the two angles
are complementary.
m A + m C = 90  .
Therefore,  A and  C are
complementary.
[C]
If today is Friday, I’m eating fish
for dinner. Today is Friday the 13th.
Therefore, I’m eating fish for dinner
tonight.
G
K
H
[D]
F
[A] EF & JI
[C] IH & IG
[B] DE & GF
[D] FH & IH
Page 4 of 4
3
x
2
If Marcus passes his Geometry test
with a at least a B, his parents will
allow him to go to Winter Formal.
Marcus gets an A on the test. So,
he will be going to Winter Formal.
© Mastery Mathematics

Geometry
Unit 4 Review
Revised Summer 08
Competency 1:
Competency 4:
1.
17. If lines are parallel => alt
interior ’s 
18. ASA
19. 3 &4 are right ’s
20. XW  XW
21. CPCTC
2. Scalene triangle
3. Obtuse triangle
4. X=20, Y=80
5. X=105, Y=75
6. 37, 48, 95
Competency 5:
Competency 2:
22. x=50 y=80
7. ABCDFE; ASA
23. x=70 y=70
8. RSTMNO; SSS
24. x = 60 y = 30
25. x = 7’
9. PQRCAB (or ∆BAC); SAS
26. x = 55, y=55
10. Not Possible
11. MNOMPO; HL
Competency 6:
Competency 3:
27. C
28. A
12. MONPOR; AAS
29. D
13. WYXWYZ; SSS

14. Can vary, either FE  CB SAS,
30. B
31. A
DA ASA or EB AAS
15. Can vary, either VY  XY SAS,
VX AAS or ZW ASA
Justification: Not all supplemental
angles form a linear pair.
16.
a)
R
S
b) Congruent
by SAS
T
P
Page 5 of 4
Q
© Mastery Mathematics

Geometry
Unit 4 Review
Revised Summer 08
Competency 1:
1.
2. Scalene triangle
Competency 4:
3. Obtuse triangle
4. X=20, Y=80
17. If lines are parallel => alt
interior ’s 
18. ASA
19. 3 &4 are right ’s
20. XW  XW
21. CPCTC
5. X=105, Y=75
6. 37, 48, 95
Competency 2:
7. ABCDFE; ASA
Competency 5:
8. RSTMNO; SSS
22. x=50 y=80
9. PQRCAB (or ∆BAC); SAS
23. x=70 y=70
10. Not Possible
24. x = 60 y = 30
11. MNOMPO; HL
25. x = 7’
Competency 3:
26. x = 55, y=55
12. MONPOR; AAS
Competency 6:
13. WYXWYZ; SSS
27. C
14. Can vary, either FE  CB SAS,
28. A
DA ASA or EB AAS
29. D
15. Can vary, either VY  XY SAS,

VX AAS or ZW ASA
16.
30. B
31. A
a)
R
S
T
P
Page 6 of 4
b) Congruent
by SAS
Justification: Not all supplemental
angles form a linear pair.
Q
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