Find each numbered angle
For problems 1-3, find each numbered angle and give a reason for each answer.
1.
2.
3.
4. Name the transformation shown in the figure below:
5. Given ΔABC with points A(1, 5),
B(6, 3) and C(8, 7). The triangle is
reflected across the y-axis to form
ΔA′B′C′. Find the point B′.
6. Given ΔABC with points A(-1, 5),
B(-2, -3) and C(2, 3). The triangle is
translated to form ΔA′B′C′ where A′
is the point (4, 2). Find the point B′.
7. Given ΔXYZ with points X(-3, 1),
Y(1, 4) and Z(5, 2). The triangle is
reflected across the x-axis to form
ΔX′Y′Z′. Find the point Z′.
8. Given ΔXYZ with points X(0, 2),
Y(0, 5) and Z(-2, 4). The triangle is
rotated 90° counterclockwise around the
origin to form ΔX′Y′Z′. Find the
point Z′.
9. Given ΔXYZ with points X(4, 0), Y(8, 0) and Z(5, 3). The triangle is rotated 180° counterclockwise around the origin to form ΔX′Y′Z′. Find the point Z′.
10. Can the following set of three sides
form a triangle? Yes or no.
a. 14, 20, 34
b. 4, 19, 4
c. 11, 5, 8
11. Find the maximum and minimum
values for the third side of a triangle
with two sides given
a. 60 and 62
b. 14 and 20
12. List the three angles of the triangle
in order from smallest to largest.
13. Find x and y in the figure given
M and N are midpoints.
14. Find x and y in the figure given
M and N are midpoints.
15. Find x in the rectangle
16. Find x in the rhombus.
17. Find x and y in the parallelogram.
For problems 18-31, if the two triangles shown are congruent, give a reason (SSS, SAS, ASA, AAS, or HL) why they are congruent and write a correct congruence statement. If there is not enough information to say the triangles are congruent, write “not congruent”.
18.
19.
20.
21.
22.
23.
24.
25.
26.
.27.
28.
29.
30.
31.
32. Find the sum of the measures of the
exterior angles of a 20-gon.
33. Find the measure of one exterior angle
of a regular 15-gon
34. The measure of one interior angle of a
regular polygon is 120°. Find the
number of sides of the polygon.
35. The measure of one exterior angle of a
regular polygon is 40°. Find the
number of sides of the polygon.
36. Find x in the diagram below:
37. Find the sum of the measures of the
interior angles of a hexagon.
38. Find the measure of one interior angle
of a regular 15-gon
39. The sum of the measures of the interior
angles of a polygon is 3240. Find the
number of sides of the polygon.
40. Find x in each diagram below.
a.
b.
For problems 41-53, find x in each figure.
41.
42.
43.
44.
45.
48.
49.
50.
51.
52.
53.
For problems 54-, find x in each figure.
54.
55. ∠1 and ∠2 are complementary.
m∠1 = 3x + 10
m∠2 = 2x
Find x.
56.
57. m∠ AOC = 130°
58. ∠1 and ∠2 are supplementary
m∠1 = 3x
m∠2 = x + 20
Find x.
59. Write the inverse, converse, and
contrapositive of the conditional
statement. Decide whether the
converse is true or false. If false,
provide a counterexample.
a. If x = 12, then x2 = 144.
b. If a number is odd, then it is divisible by three.
c. If a figure is a square, then all of its angles are right angles.
60. Write an indirect proof to show that a
triangle can have at most one obtuse
angle.
61. For each pair of points, find the
midpoint and length of the segment
connecting the points.
a. (-3, 1) and (4, 4)
b. (-1, 2) and (-7, -6)
For problems 62-63, use the Pythagorean Theorem to find the length of x.
62. 9
63.
For problems 64-68, find the area of each figure.
64.
65.
66.
67.
For problems 68-69, find the area and perimeter of each figure.
68.
69.
70. Find the area of the shaded region.
-----------------------
35°
4
3
2
1
55°
14
2x + 8
40°
y
65°
M
N
Z
1
4
35°
3
85°
2
24
x
N
M
y
78°
31°
21
10
18
Y
Z
X
2
55°
40°
1
45°
3
4
80
50
x
I
J
H
K
D
X
Y
W
V
B
A
D
C
J
M
K
L
W
X
Y
Z
N
O
A
B
X
Y
V
Z
W
B
A
D
C
E
H
F
G
D
G
F
E
E
H
F
G
W
X
Y
Z
P
T
Q
R
A
B
C
D
60
x
E
y
20
7
25
x
20
x
60
40
70
x
30
100
x
130
120
100
x
80
33
20
x
B
A
O
x + 5
75
9x
x + 30
x + 50
4x + 40
25
5x
25
x
x + 20
5x - 2
3x + 22
4x
2x + 10
70
55
x + 15
3x - 10
4x
50
50
100
x + 40
5x + 20
2x + 50
4x - 30
45
4x - 10
2x - 5
C
12
x
7
16
x
5
8
14
15
8
17
12
6
9
20
22
4
7
4
35
29
8
15
12
8
9
6
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