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GPS Geometry
Final Exam Review
Unit 1 – Geometry Gallery
Name:
Multiple Choice (2 points each) Choose the best answer.
1. Find LP. [Note: Figure not drawn to scale]
(A) LP = 4
L
M
(B) LP = 5
P
(C) LP = 10
4
(D) LP = 8 6
5
N
O
2. Opposite angles of a parallelogram are _________________.
(A) Sometimes congruent
(B)
Always congruent
(C) Complementary
(D)
Supplementary
3. Given square MNOP. The perimeter of MNOP is 72cm, NO = 2x + 6. Find x.
(A) x = 15
(B) x = 12
(C) x = 9
(D) x = 6
4. Complete the congruence statement GJH  ___ by ____.
(A)
GJH  IJH by SAS
(B)
GJH  IHJ by SAS
(C)
GJH  IJH by HL
J
(D)
GJH  IHJ by HL
I
G
H
5. The sides of a triangle are 12, 7 and x. Which of the following is a possible value
for x?
(A) 19
(B) 5
(C) 8
(D) 21
6. E is the midpoint of AC and BD . Choose the true statement.
(A) AEB  DEC by ASA
A
(B) AEB  DEC by SAS
(C) AEB  CED by ASA
E
B
D
(D) AEB  CED by SAS
C
7. Given Q  V and the figure shown, which statement is NOT necessarily true?
(A)
QAM  VWM
(B)
QWA  VAW
(C)
QAM  VMW
(D)
WAM is isosceles
V
Q
M
A
W
(C) circumcenter
(D) centroid
8. The medians of a triangle concur at the
(A) orthocenter
(B) incenter
9. Which points of concurrency may lie outside the triangle?
(A) orthocenter and the circumcenter
(B)
circumcenter and incenter
(C) centroid and incenter
(D)
centroid and orthocenter
10. In CAT , C is 54 and T is 36. What is the longest side of the triangle?
(A) CA
(C) CT
(B)
AT
(D)
cannot be determined
Free Response
Answer completely.
11. Given the diagram as shown, list the segments, AB, BC, AC, DC, and BD , in
order of size starting with the smallest.
A
B
30
D
C
12. Use the information in the diagram to solve for x. Show your work.
13. The diagonals of a quadrilateral are perpendicular to each other, what kind(s) of
quadrilateral do we have?
14. In a certain regular polygon, the measure of an interior angle is equal to the
measure of an exterior angle. How many sides does the polygon have?
15. Find the value of each variable in the parallelogram.
16. Write the contrapositive of the following statement.
“If we go to bed late, then we will not pass the test.”
17. Given: JL  KP , JL || KP
Prove: JLK  PKL
18. Postulate: If two lines are cut by a transversal so that corresponding angles are
congruent then the lines are parallel.
Theorem: If parallel lines are cut by a transversal then the alternate interior angles
are congruent.
a. State the converse of the theorem.
b. Prove the converse of the theorem.
a
1
2
3
b
19. Given the diagram below with GE, GD and GF are perpendicular bisectors of the
sides of the triangle.
C
G
F
A
D
E
B
a. G is the ____________________ of the triangle.
b.
ABC is an obtuse triangle. How do you know this from the diagram without
measuring the angles?
c. If G is on ABC what kind of triangle would it be?
Higher-level Standardized Test Questions (4 points each)
20. Given the diagram below. mD = 3x + 4, find x
(A) x = 80
(B) x = 22
(C) x = 66
(D)
x = 106
3
21. Given the diagram below, find mE.
(A) mE = 130
(B) mE = 65
(C) mE = 50
(D) mE = 115
22. Which is the inverse of the following statement?
“If it is Thursday, then we eat pizza.”
(A) If we do not eat pizza, then it is not Thursday.
(B) If we eat pizza, then it is Thursday.
(C) If it is not Thursday, then we do not eat pizza.
(D) If it is not Thursday, then we eat lasagna.
23. Which is a counterexample for the following statement?
“If it grows, then it is alive.”
(A) A dead tree
(B) The national debt
(C) A baby boy (D) A blue whale
24. Given the diagram at right, which theorem or postulate proves 3  7?
(A) Congruent Complements Theorem
(B) Side-Angle-Side Postulate
(C) Vertical Angles Theorem
(D) Corresponding Angles Postulate
Solutions:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
B
B
D
A
C
D
C
D
A
C
DC, BD, BC, AB, AC
x=14
kite, rhombus, square
4
b=90, c=80, d=100
If we pass the test, then we did not go to bed late.
JLK  PKL
KL  LK
JLK  PKL
Alternate Interior Angles Theorem
Reflexive Property
SAS
18. a) If two lines are cut by a transversal so that alternate interior angles are
congruent, then the lines are parallel.
b) Given: 2  3 ; Prove: a b
2  3
2  1
1  3
a b
Given
Vertical Angles Theorem
Transitive Property of Congruence
Postulate
19. a) circumcenter
b) the circumcenter is outside the triangle
c) a right triangle
20.
21.
22.
23.
24.
B
D
C
B
C