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FINAL REVIEW
S
.Q
1. Name four coplanar points.
.T
2. What is the intersection of ST and TR ?
3. What is the intersection of
TR and plane P?
4. What is the intersection of
SM
N
P
R
.
M
and TR ?
5. Name a point between S and M?
6. Find AB if the coordinate of A is -5 and the coordinate of B is 17. Locate the
midpoint of AB ?
2x - 5
x+3
7. If JL = 19, find the value of x?
8.
J
K
SQ is a bisector of  RSP. Solve for y and find m  QSR?
L
P
(5y + 3)˚
Q
(7y - 11)˚
R
S
9. Find the slope of a line perpendicular to each line:
a. y = 4x + 7
m = _________
1
b. y = - x – 3
8
m = ____________
10. Determine if the corresponding lines are parallel, perpendicular or neither, given
their slopes:
a. -
1
and -2
2
b.
5
3
and 3
5
a. _________________
b. ________________
c. 1 and 1
d. 1 and -1
c. __________________
d. _____________________
11. Find x and y. Then find m  1?
12. Find:
a. Two pairs of vertical angles.
b. Two pairs of supplementary angles.
c. Name two pairs of angles which are congruent.
(5x)
1 ˚
(17x +
y
4) ˚
˚
1
2
4
3
13. One angle is twice as large as its complement. Find the measure of both angles?
14. The measure of a supplement of  1 is six times the measure of a complement of
 1. Find m  1, its supplement and its complement?
15. Name the property that justifies each statement:
i)  Z   Z
__________________________
ii) If ST  QR , then QR  ST .
__________________________
iii) If 2x + y = 5 and x = y, then 2x + x = 5 __________________________
iv) If m  A = 15˚, then 3m  A = 45˚.
__________________________
v) If  1   2 and  2   3, then  1   3. ______________________
vi) QR = QR
__________________________
vii) 2(3x + 5) = 6x + 10
__________________________
16. Find the value of x, m  1:
130˚
70˚
x˚
1˚
1
17. Give an example of an obtuse and isosceles triangle. Show the measure of all its
angles.
18. If l || m, find x?
(2x)˚
(5x)˚
l
m
(5x + 40)˚
(3x – 2)˚
19. If m || l, find all labeled angles:
1
x = _________
2
3
4
m  1 = _______
m  2 = _______
m  3 = _______
5
6
(5x - 40)˚
m
l
m  4 = _______
m  5 = _______
m  6 = ________
20. Find m  B, if AD || BC .
A
B
50
C
D
120
21. In  ABC, find AB:
x
A
C
x + 15
2x - 5
B
22. In  ABC, the points D, E and F are midpoints. AC = 10cm, AB = 12cm and BC = 4
cm. Find the three midsegments FE, FD and DE:
B
D
E
A
C
F
Find the variables:
z
x 

23.
(z – 13) w


24.
x (x – 28)

y
(z + 10)

25.
(2y – 1)

26.
y
11
y
y
x
30
x
12
27.
28.
40
x
9 3
x
60
30
y
y
29.
x
45
14 2
30. Write the similarity statement and name the postulate or theorem used:
a.
W
b.
F
2
V
H
3
S
4
J
A
G
6
K
T
A
c.
d.
3
3
P
30
J
32
5
B
P
J
60
40
R
22
Q
8
C
K
45
L
A
e.
12
24
10
16
C
D
B
18
E
31. List the sides of each triangle in order from shortest to longest:
a.
b.
O
G
28
45
75
M
110
F
N
H
32. In  ABC, if m  C < m  b; then side AC > ___?___
A
a
B
c
b
C
33. Calculate the indicated trigonometric ratios:
a.
b.
C
2
C
3
B
1
1
10
A
sin A = ________
cos B = ________
tan A = ________
5
B
A
sin A = _______
cos B = _______
tan A = ________
34. A surveyor is 90 feet from the base of the world’s tallest fountain at Fountain Hills,
Arizona. The angle of elevation to the top of the column of water is 29.7. His angle
measuring device is at the same level as the base of the fountain. Find the height of the
column of water to the nearest 10 feet?
35. Find the values of x and y. Round your answer to the nearest tenth.
a.
b.
x
.O
x
50
y
y
40
x = _______, y = _______
c.
88
x = _______, y = _______
d.
12
x
.
P
8
16
3
x
x = _______
x = _______
Assume the lines that appear to be tangents as tangents. Find the value of each variable.
Round answers to the nearest tenth.
36.
37.
7
95
.
10
x
x
8
72
y
x = ________, y = ________
x = ________
38. If TW is the median, find ST:
T
x + 10
S
2x + 3
W
3x - 1
V
ST = ____________
39. Write the equation of a line with slope 3 and y-intercept of –5. Write equation of two
lines  to that line. Write the equation of two lines || to that line?
40. Use the distance formula along with the slope formula to show that  ABC is an
isosceles right triangle with coordinates A(-2, 3), B(4, 1) and C(-2, -1).
Fill in the blanks:
41. The sum of the exterior angles of a decagon is ________.
42. The sum of the interior angles of an octagon is _________.
43. The measure of each interior angle of a regular hexagon is ________.
44. The measure of an exterior angle of a regular hexagon is ________.
45. Find the perimeter of an isosceles triangle whose altitude is 20 and base is 10?
20
10
46. Find all the angles of a parallelogram with two opposite angles (10x – 5) and (5x +
5)?
47. If  B of a parallelogram ABCD is 100, how large is  C?
48. If a || b; find  1?
2 1
3
4
a
36
b
NOTE: APOTHEM is the  distance from the center to a side of a regular polygon.
49. Find the area and perimeter of a regular pentagon that has apothem 24.3 cm and side
35.4 cm. Round your answer to the nearest tenth.
Find the area of each regular polygon to the nearest tenth:
50.
51.
10 in.
8 cm
Find the value of the variables:
52.
53.
6
30
x
z
y
16
y
x
9
x = _____, y = _____, z = _______
54.
x = _____, y = _____, z = _______
x
y
9
6
z
x = _____, y = _____, z = _______
55. Find the perimeter and area of a regular heptagon, whose apothem is 4.
z
56. Find x, if AB = 40.
57. If AC = 6, find AB?
C
A
60˚
x
30˚
B
C
B
A
Polygon interior angle sum = (n – 2)* 180˚
Polygon exterior angle sum = 360˚
58. Find the measure of each interior angle of a regular octagon?
59. How many sides does a regular polygon have if the measure of its interior angles is
1440˚?
60. What is the measure of each interior angle of a regular pentagon?
A
61. Given: m  A = 45˚, m  B = 90˚, m  C = (2x + 10)˚,
m  D = 200˚, m  E = 8x˚.
a.
b.
c.
d.
Name the figure?
Find the interior angle sum?
Find the exterior angle sum?
Find x?
E
B
O
D
C