Download sample Geometry Test

Geometry Review
Here are some formulas and concepts that you will need to review before working on
the practice exam.
Triangles
o Perimeter or the distance around the triangle is found by adding all of the
sides, or, P = a + b + c, where P is the perimeter and a, b, and c are the
sides of the triangle.
a
c
b
o Area is found by taking half of the product of the base and the height. Or,
1
A
bh , where A is the area, b is the base and h is the height. Notice
2
that the height always forms a right angle with the base and, in some
cases the height may lie outside the triangle.
h
h
b
b
i
o The sum of the three angles of any triangle
n is always 180 .
o Pythagorean Theorem states that for any right triangle, a2 b2 c 2 ,
where c is the hypotenuse, and a and b are the other two sides of the right
triangle.
c
a
b
Rectangles
o Perimeter or the distance around the rectangle is found by adding all the
sides or by using P 2L 2W where P is the perimeter, L is the length
and W is the width.
o Area is given by A
the width.
L W , where A is the area, L is the length and W is
W
L
Revised on 11/2/2009
Page 1 of 10
Squares
o Perimeter or the distance around the square is found by multiplying a side
by 4, or, P = 4a, where P is the perimeter and a is the length of a side.
o Area is found by squaring a side, or, A
the length of a side.
a2 , where A is the area and a is
a
Circles
o Circumference or the distance around the circle is found by using
C 2
r , or C
d , where C is the circumference, r is the radius, d is
the diameter and can be approximated as 3.14.
o Area is given by A
r 2 , where A is the area, r is the radius, and
approximated as 3.14.
is
o If instead of the radius r, the diameter d is given, divide d by 2 to find the
radius. In other words, r = d / 2.
r
r
d
Similar Triangles
o Two triangles are similar if they have the same “shape”, but one is just a
reduction or enlargement of the other (like on a copy machine).
D
A
B
C
F
E
o
ABC
DEF means that triangles ABC and DEF above are similar. In
similar triangles the ratios of corresponding sides are equal and the
corresponding angles are equal. Therefore for the above triangles we
have:
AB
DE
Revised on 11/2/2009
AC
DF
BC
and
EF
A
D,
B
E,
C
F.
Page 2 of 10
Parallel Lines
For the parallel lines L1 and L2, all the given pairs of angles are congruent.
2
3
6
7
L1
1
4
5
L2
8
o Alternate Interior Angles:
 4 and 6
 3 and 5
o Alternate Exterior Angles:
 1 and 7
 2 and 8
o Corresponding Angles:
 1 and 5
 2 and 6
 3 and 7
 4 and 8
o Vertical Angles:
 1 and 3
 2 and 4
 6 and 8
 5 and 7
Angles
180
o A flat angle is 180 .
o A square (right) angle is 90 .
90
Key for the Sample Problems
1.
4.
7.
10.
13.
16.
19.
22.
25.
28.
Revised on 11/2/2009
B
B
D
B
D
D
D
C
B
A
The sample problems start on the next page.
2.
D
5.
D
8.
A
11.
A
14.
A
17.
B
20.
A
23.
D
26.
C
29.
B
3.
6.
9.
12.
15.
18.
21.
24.
27.
30.
C
A
A
A
B
C
A
C
B
C
Page 3 of 10
Geometry Sample Problems
You will find the answers on the bottom of page 3 of this packet.
1. Find the perimeter of the rectangle.
8 ft 9 in
A.
C.
177 in
14.9 ft
B.
D.
29 ft 6 in
29.8 ft
A.
C.
16.8 ft
31.8 ft
B.
D.
200 in
31 ft 6 in
A.
C.
10 ft 6 in
21 ft
B.
D.
126 in
21.2 ft
A.
C.
40
60
B.
D.
140
120
A.
C.
110
23
B.
D.
47
157
6 ft
2. Find the perimeter of the rectangle.
9 ft 9 in
6 ft
3. Find the perimeter of the rectangle.
7 ft 6 in
3 ft
4. Find the measure of angle x.
103
x
37
5. Find the measure of angle x.
110
47
Revised on 11/2/2009
x
Page 4 of 10
6. Find the measure of angle x.
x
A.
C.
71
119
B.
D.
60
109
60
49
7. The perimeter of the triangle is 145 inches. Find the length AC .
A.
C.
B
2x
A
28 inches
56 inches
B.
D.
145 inches
61 inches
x
C
2x + 5
8. The perimeter of the triangle is 135 meters. Find the length AC .
A.
C.
B
2x
A
x
2x + 5
57 meters
52 meters
B.
D.
26 meters
135 meters
C
9. The perimeter of the triangle is 122 feet. Find the length AB .
A.
C.
C
47 ft
50 ft
B.
D.
25 ft
100 ft
B.
D.
225 sq in
1000 sq in
2x
x
A
x + 22
B
10. The perimeter of a square is 60 inches. Find the area.
A.
C.
Revised on 11/2/2009
3600 sq in
900 sq in
Page 5 of 10
11. The perimeter of a square is 100 centimeters. Find the area.
A.
C.
625 sq cm B.
2500 sq cm D.
10,000 sq cm
1000 sq cm
12. The perimeter of a square is 40 meters. Find the area.
A.
C.
100 sq m
2500 sq m
B.
D.
1600 sq m
1000 sq m
B.
D.
126
117
B.
D.
47
147
B.
D.
77
157
13. Lines L1 and L2 are parallel. Find the measure of x.
L1
63
x
A.
C.
63
153
L2
14. Lines L1 and L2 are parallel. Find the measure of y.
L1
A.
C.
133
43
133
y
L2
15. Lines L1 and L2 are parallel. Find the measure of x.
77
L1
A.
C.
103
13
x
L2
Revised on 11/2/2009
Page 6 of 10
16. Find the area of the figure.
10 in
15 in
15 in
A.
C.
800 sq in
500 sq in
B.
D.
650 sq in
575 sq in
A.
C.
800 sq m
805 sq m
B.
D.
900 sq m
875 sq m
A.
C.
600 sq in
525 sq in
B.
D.
550 sq in
575 sq in
20 in
40 in
17. Find the area of the figure.
15 m
5m
15 m
30 m
40 m
18. Find the area of the figure.
15 in
10 in
20 in
5 in
30 in
19. Find the length of the diagonal of the rectangle based on the given information.
5 in
A.
C.
19 in
15 in
B.
D.
17 in
13 in
12 in
Revised on 11/2/2009
Page 7 of 10
20. Find the length of the diagonal of the rectangle based on the given information.
A.
C.
15 ft
21 ft
B.
D.
18 ft
16 ft
9 ft
12 ft
21. Find the length of the diagonal of the rectangle based on the given information.
A.
C.
6m
10 in
15 in
B.
D.
17 in
13 in
B.
D.
10
10 ½
B.
D.
4
4½
8m
22. The two triangles are similar. Find the length of DE .
E
A.
C.
12
8½
9
F
D
B
8
6
A
C
9
23. The two triangles are similar. Find the length of DE .
A.
C.
D
A
3
5
3½
5
B 4
C
Revised on 11/2/2009
E
6
F
Page 8 of 10
24. The two triangles are similar. Find the length of EF .
D
A.
C.
6
11
9
B.
D.
11 ½
12 ½
F
E
A
8
4
B
6
C
25. The diameter of a circle is 10 inches. What is its circumference?
A.
C.
between 15 and 16 inches
between 47 and 48 inches
B.
D.
between 31 and 32 inches
between 28 and 29 inches
26. The diameter of a circle is 1 centimeter. What is its circumference?
A.
C.
between 1 and 2 cm
between 3 and 4 cm
B.
D.
between 2 and 3 cm
between 4 and 5 cm
27. The radius of a circle is 5 inches. What is its circumference?
A.
C.
between 15 and 16 inches
between 47 and 48 inches
B.
D.
between 31 and 32 inches
between 28 and 29 inches
28. Find the area of the triangle.
3.5 in
A.
C.
7 sq in
28 sq in
B.
D.
14 sq in
Can’t be done
4 in
Revised on 11/2/2009
Page 9 of 10
29. Find the area of the triangle.
A.
C.
6.75 sq m
27 sq m
B.
D.
13.5 sq m
Can’t be done
A.
C.
12 sq in
6 sq in
B.
D.
15 sq in
10 sq in
4.5 m
6m
30. Find the area of the triangle.
5 in
3 in
4 in
Revised on 11/2/2009
Page 10 of 10