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Name: ________________ Date: ___________
Review
Geometry Exam Review
1st Semester
1. If the pattern indicated below is continued,
what would be the total number of cubes in the
8th stage of the pattern?
6. If ∠ = 25° and ∠ = 51°, then
what is the measure of ∠?
1
1+4=5
1 + 4 + 9 = 14
2. Determine whether the triangles are similar.
If so, write a similarity statement and the
postulate or theorem that justifies your answer.
&
'
7. ∠ = (2 + 9)° and ∠ = (6 −
8)° and ∠ = 65°. Find ∠ and
∠.
35°
%
3. Let D be between E and F. Use the Segment
Addition Postulate to solve for n.
= 2 + 6
= 3 + 4
= 20
8. If angle "# is acute and angle $" is right,
then angle $# is what kind of angle?
4. Find the distance between the points
(–5, –4) and (2, 2).
$
5. Determine whether the triangles are similar.
If so, write a similarity statement and the
postulate or theorem that justifies your answer.
6
27
(
9
18
)
#
"
9. When two parallel lines are crossed by a
transversal, alternate interior angles are always
_______.
10. In the figure shown, ∠% = 124°.
Which of the following statements is false?
%
15. Find the area of a circle with radius 14 cm.
Use 1 = 3.14.
&
16. Find the circumference of the circle. Use
1 = 3.14.
'
A) ∠&' and ∠' are adjacent angles
B) ∠%& and ∠' are supplementary
angles
C) ∠%& = 56°
D) ∠&' = 124°
11. Solve for x:
575.
17. Rewrite the statement in if-then form.
“Every triangle has three sides”
(4 + 128)°
(4 + 20)°
18. “If I get a chance, I will succeed.” In this
conditional statement, the underlined portion is
____.
12. Solve for x:
(2 + 28)°
(4 + 20)°
13. The coordinates of ∆%&' are given as
%(2,1), &(3,5), and '(6,3). ∆%&'~∆./0.
Coordinates given are .(8,4) and /(12,20).
What are the coordinates of Z?
19. Complete the following statement as stated
by the Point, Line, and Plane Postulates: Skew
lines ___ intersect in exactly one point.
20. Which of the following is an example of the
Transitive Property?
A) + 3 = 3 + B) If + 3 = 2 and 2 = −4, then
+ 3 = −4
C) If 2 = − 4, then − 4 = 2
D) If = 3, then − 4 = 3 − 4
14. Name an angle adjacent to ∠&'
21. Identify the property of congruence. “If
&
'
%
' ≅ and ≅ , then ' ≅ .
22. Determine whether the dilation from Figure
A to Figure B is a reduction or an enlargement.
Then find its scale factor.
27. In the figure, :|| and r is a transversal.
Which of the following is not necessarily true?
D
1
4
5
&
8
2
3
:
6
7
%
A) ∠7 ≅ ∠4
B) ∠2 ≅ ∠6
C) ∠5 ≅ ∠3
D) ∠8 ≅ ∠2
23. ∠1 and ∠2 are a linear pair. If ∠2 = 67°,
then find ∠1.
24. Name a pair of parallel planes?
)
28. Find the slope of the line passing through
the points A(8,6) and B(2,3).
29. Find the geometric mean of 8 and 12.
Leave your answer in simplest radical form.
B
?
(
C
?
A) 2 = − @ − 7
#
6
30. A line parallel to 2 = @ − 7 is ________.
@
B) 2 = ? + 2
"
@
C) 2 = − ? + 7
?
D) 2 = @ + 1
"#
25. Find ∠1 in the figure below. 788889
6 and 78889
are parallel.
62°
6
"
1
#
31. The measures of the angles in ∆%&' are in
the extended ratio of 2: 3: 4. Find the measures
of the angles.
32.
&
18
78889
26. Find ∠1 in the figure below. 788889
6 and "#
are parallel.
69° 6
12
6
3
"
1
#
'
%
39. Find the value of x.
33. )B is a midsegment of ∆%&'.
%
85°
)
60°
2°
'
B
125°
40. Find the value of x.
&
63°
34. A line perpendicular to 2 = −4 + 2 is
_________.
A) 2 = −4 − 2
B) 2 = 4 + 2
°
120°
E
C) 2 = − F + 1
E
D) 2 = + 1
F
41. What is the perimeter of ∆)BC if the scale
@
factor of ∆./0 to ∆)BC is F, and the perimeter
35.
Which best describes the relationship
between Line 1 and Line 2.
Line 1 passes through (-1, 7) and (-3, 10)
Line 2 passes through (-2, 9) and (-5, 7)
36. Classify ∆)BC
of ∆./0 is 36?
42. Find the measure of the interior angles to
the nearest tenth. (Drawing is not to scale).
(4 + 1)°
B
8
( − 1)°
8
)
(2 − 1)°
C
8
37. Name an obtuse triangle.
&
43. The measure of ∠& is _____.
35° 55°
51°
%
30°
115° 65°
60°
'
38. Write the conditional, converse, inverse,
and the contrapositive of the statement “A poet
is a writer”
130°
&
44. Isosceles triangle )BC has legs )B and BC,
and base )C. If )B = 8 ? + 60, BC = 10 ? −
4, and )C = 4 + 7. Find the value of x.
49. Which postulate or theorem can be used to
determine the measure of "$?
#
170
45. If ∆%&' ≅ ∆, AB=23 feet, ∠& = 19°,
and ∠ = 41°, which of the following
statements is false?
A) ∠' ≅ ∠
B) '% = C) %& = D) ∠ = 120°
46. If ∆%&' ≅ ∆6" and ∆6" ≅ ∆CB, then
∆%&' ≅ ∆CB. This illustrates which property
of congruence?
240
"
J
$
170
K
50. What is the measure of each base angle of
an isosceles triangle if its vertex angle
measures 38 degrees and its 2 congruent sides
measure 18 units?
38°
18
18
47. What must be true in order for ∆%&' ≅
∆' by the SAS Congruence Postulate?
&
'
51. Find the values of x and y.
%
48. Refer to the figure shown. Which of the
following statements is true?
&
2
'
112°
&'||
&' = A) ∆&' ≅ ∆ by SAS
B) ∆&' ≅ ∆ by ASA
C) ∆&' ≅ ∆ by ASA
D) ∆&' ≅ ∆ by ASA
52. ∆%& ≅ ∆'&. Name the theorem or
postulate that justifies the congruence.
%
&
'
53. An isosceles right triangle is placed in a
convenient position in the first quadrant of a
coordinate plane. Which is the missing label for
the vertex?
2
?
57. Given that M = (ℎWXUWNℎℎSUYSDZ and
Q = (UUTNSONPT2[SDWWNℎNUON, write a
statement from the following symbolic notation.
~M ⋀ Q.
58. Determine if the statements below are true
or false according to the diagram. Please write
out “true” or “false” clearly.
(0,0)
(W, 0)
Plants
Flowering
Plants
Bushes
Roses
54. Given 788889
' is the perpendicular bisector of
)C. Which statement is true?
'
)
B
C
a) No bushes are flowering plants.
b) Some roses are not flowering
plants.
c) Some flowering plants are bushes.
59. For the triangle shown, VS=5 and VQ=6.
Then PQ=____.
A) D is the midpoint of )C
B) ∠)'C is a right angle
C) '_|_)C
D) C = 'C
#
$
"
6
J
55. Given that M = 5N5OOP2 and Q =
5N5OℎSNSPNO5TU, write a statement from the
following symbolic notation. ~M → Q
60. Refer to the figure. The longest side is
_____.
70°
56. In the figure (not drawn to scale), 8888889
bisects ∠C, ∠C = 13 − 31, and
∠ = + 53. Solve for x and find
∠C.
C
105° C
65°
30°
61. Which side lengths allow you to construct a
triangle?
A) 7, 2, and 2
B) 6, 8, and 10
C) 2, 3, and 8
D) 4, 1, and 9
62. Two sides of a triangle have sides 6 and 9.
The length of the third side must be greater
than ___ and less than ___.
63. Which of these lengths could be the sides
of a triangle?
A) 8 cm, 20 cm, 12 cm
B) 12 cm, 18 cm, 4 cm
C) 18 cm, 12 cm, 5 cm
D) 20 cm, 8 cm, 13 cm
66. Solve for x.
83°
(6 + 12)°
( + 29)°
67. Lines W and d intersect lines e and T in the
figure below. Circle the statements that
could be used to prove that W||d and e||T.
5
8
64. Refer to the figure. Choose the correct
statement.
10
13
75° 60°
7
W
d
4
6
1
3 2
12 9
10
11
T
e
∠1 ≅ ∠5, ∠12 and ∠7 are supplementary
∠1 ≅ ∠7, ∠5 and ∠11 are supplementary
∠3 ≅ ∠6, ∠5 ≅ ∠9
10
∠1 and ∠6 are supplementary, ∠6 and
A) > 13
B) = 13
C) < 10
D) 10 < < 1
∠9 are supplementary
∠5 ≅ ∠7, ∠7 and ∠12 are supplementary
Continue on next page for proof practice.
65. Which figure below is not a polygon?
A)
B)
C)
D)
Name: ________________ Date: ___________
Review
68. Complete the proof by filling in the missing steps.
j
GIVEN: ∠1 ≅ ∠3
PROVE: ∠VZX ≅ ∠YZW
J
∠1 ≅ ∠3
∠1 = ∠3
∠J0. = ∠1 + ∠2
∠J0. = ∠3 + ∠2
∠/0j = ∠3 + ∠2
∠J0. = ∠/0j
∠J0. ≅ ∠/0j
69.
GIVEN:
.
_______
_______
_______
_______
_______
_______
_______
1
2
B is the midpoint of %'
'
& || %
PROVE:
/
3
0
& ≅ %
∠ ≅ ∠
B is the midpoint of %'
_____
%& ≅ &'
_____
& ≅ %
_____
&k%
_____
∠&% ≅ ∠'&
∆&% ≅ ∆'&
∠ ≅ ∠
_____
_____
_____
&
%
70. Fill in the missing steps.
M
Given: ‖ , ∠8 ≅ ∠15
Prove: M‖Q
‖
∠4 ≅ ∠8
∠8 ≅ ∠15
∠4 ≅ ∠15
M‖Q
_____
_____
_____
_____
_____
1
3
5
7
Q
2
15 16
4
6
8
14
9
11
13
10
12