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Geometry
1st Semester Review
Name:________________________
1. State the converse, inverse and contrapositive of the following statement:
“If R is acute, then mR is less than 90.”
Converse:_______________________________________________________________
Inverse:_________________________________________________________________
Contrapositive:___________________________________________________________
2. What is the appropriate conjecture based on the given if…then statement?
Given: If it is Monday, then tomorrow is Tuesday. It is Monday.
3. Find a counterexample for the following conjecture.
x3  0
Conjecture:
4. Find the coordinates of M , the midpoint of AB .
A(-2, 4)
B(10, -6)
a
5. If a // b, m1  4x 12 , and m2  9x  58 , find m1 .
b
1
2
6. Find the mx .
35
x
25
7. The perimeter of FED is 53. By solving for x , determine whether FED is scalene,
isosceles, or equilateral.
F
17
x + 12
E
3x
D
8. Which three lengths could form a triangle? Explain why.
A. 6, 6, 15 ___________________________________________________________
B. 7, 10, 12___________________________________________________________
C. 8, 12, 20___________________________________________________________
9. Given B  D and BD bisects AE at C . By what method is ACB  ECD ?
D
A
C
E
B
10. Find the sum of the interior angles of a heptagon.
11. For lunch, Avery can choose either a hamburger (H) or a burrito (B) and either a
soda (S) or water (W). What is the outcome set for the lunches he could get?
12. Determine whether each situation involves a permutation or a combination.
A. 6 books selected from a group of 15.
B. arrangement of 6 CD’s on a shelf.
13. Cami has 4 kinds of lettuce growing in her garden. How many different salads can
she make using 2 of the types of lettuce?
14. How many different ways can 11 different candidates finish in first, second and third
places in an election?
15. Which of the following algorithms are equivalent?
I.
Given two lines, draw a transversal. If the alternate interior angles are equal,
then you have the answer you are looking for.
II.
Given two lines, compare their slopes. If they are equal, then you have the
answer you are looking for.
III.
Given two lines, compare their slopes. If they are negative reciprocals, then
you have the answer you are looking for.
16. In the figure, what point is collinear to F and J?
I
G
H
F
J
M
L
17. In the diagram, name a pair of congruent angles.
A
D
C
E
B
18. What is the complement of 37 ? What is the supplement of 37 ?
Complement:
Supplement:
19. Find the measure of ABC .
C
3x + 5
A
7x + 25
B
D
20. Given RST  QST and RS  QS . Which postulate can be used to prove that
STR  STQ ?
S
R
T
Q
21. Find the sum of the measures of the exterior angles of an octagon.
22. If AB  15 and AC  31, find BC .
A
B
C
23. What symbol is used to indicate the following:
A. two line segment are parallel _______________
B. two line segments a perpendicular___________
C. two line segments are congruent_____________
24. What word describes an angle
A. whose measure is greater than 0 and less than 90 _______________
B. whose measure is equal to 90 _______________
C. whose measure is greater than 90 and less than 180 _____________
D. whose measure is equal to 180 ______________
25. Identify the hypothesis and conclusion of this conditional statement: “If two lines
meet to form non-adjacent, non-overlapping angles, then they form vertical angles.”
A. hypothesis: _______________________________________________________
_________________________________________________________________
B. conclusion:
_____________________________________________________
_________________________________________________________________
26. The measures of two angles of a triangle are 43 and 56. What is the measure of
the third angle?
27. The measure of a base angle of an isosceles triangle is 57. What is the measure of
the vertex angle?
28. Find the value of x.
x
75
20
29. In TUV , mT  4x  6 , mU  x  5 , and mV  3x 19 . List the angles from
largest to smallest.
30. Choose the correct statement.
A. m  1 < m  3
B. m  1 = m  3
C. m  1 > m  3
1
2
3
4
31. Define the following terms:
A. Altitude __________________________________________________________
B. Median __________________________________________________________
C. Perpendicular bisector_______________________________________________
32. If EIF  FIG, then what is the best description of IF?
E
F
G
D
I
H
33. If mABD = 35 and mABC = 120, find mDBC.
A
D
B
C
34. Given SQ bisects RST. Find mQSR if mTSR = 72.
T
Q
S
R
35. Refer to the figure at the right to answer the following questions.
A. Which two pairs of angles are same side interior angles?
1
B. Which two pairs of angles are alternate interior angles?
2
C. Which four pairs of angles are corresponding angles?
36. Given a // b. Find m4.
a
b
4
32
37. If a // b and m9 = 4x + 12 and m5 = 6x – 4, then find the value of x.
a
b
9
5
4
3
5
6
8 7
38. Given that TP  KO and P  O. Name one additional pair of corresponding parts
that needs to be congruent in order to prove STP  MKO by SAS.
K
T
O
M
P
S
39. Given ABC  XYZ, AB = 17, YZ = 24, and XY = 7x – 4. Find the value of x.
40. List the properties of rectangles.
41. WXYZ is a rhombus. If XZ  15 , then find OZ .
W
X
O
Z
Y
42. Given: parallelogram ABCD as marked. Find BC.
A
12
D
9
B
C
43. Fill in the blanks for the characteristics of a rhombus.
A. The sides of the rhombus are ________________________.
B. The diagonals of the rhombus are _____________________ and _____________.
44. Given parallelogram LOVE , mO  9x 15 and mE  4x  5 . Find mV .
L
O
E
V
45. If MATH is a square, find mMTH .
M
H
A
T
46. Fill in the blanks for the characteristics of an isosceles trapezoid.
A. The diagonals are___________________________________________________
B. The bases are ______________________________________________________
C. The legs are _______________________________________________________
D. The base angles are _________________________________________________
47. If ABCD is a trapezoid with bases of 6 and 12, what is the measure of its median?
48. Find the slope of a line passing through (-3, 7) and (5, -9).
49. Graph the line with a slope of 2 passing through point R  0, 5 .
50. What is the slope of the line perpendicular to a line with slope
4
?
7