Download Honors Geometry Unit #2 Lesson #5 Vertical Angles – nonadjacent

Honors Geometry
Unit #2 Lesson #5
Vertical Angles – nonadjacent angles formed when lines intersect.
2
1
4
1 and 3 are vertical angles.
3
2 and 4 are vertical angles.
Theorem: Vertical angles are congruent.
Honors Geometry
Unit #2 Assignment #5
1. Use the diagram to the right to answer the following questions.
a. If m1 = 20°, find m2 and m3.
b. If m1 = 110°, find m2 and m3.
c. If m1 = 63°, find m2, m3, and m4.
d. If m1 = x°, find m1, m2, m3, and m4 in terms of x.
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1
3
4
2. True or False. If a statement is true, explain why it is true. If a statement is false, provide a
counterexample.
a. If two angles are vertical then the measure of each angle is 45°.
b. If two angles are vertical and supplementary, then they are right.
c. If two angles are vertical then the measure of each angle is 90°.
3. Find the measure of each numbered angle below.
a.
b.
1 123°
2 3
6
7 33°
8
10
9
147°
11
12 60°
13
4
5
  

4. In the diagram below AE  GD , XB bisects AXC, and XH bisects AXG. Find the
measure of each of the following angles.
A
B
a. BXC
H
b. AXD
C
c. CXD
36°
d. GXF
e. HXG
G
f. HXD
X
g. FXB
F
h. FXD
E
5. Find the measure of each angle in the diagram.
2
1
a.
m2  x  20, m4  x  12
5
2
b. m1  20 x 2  72, m4  60 x  28
c. m2  13 x  y, m3  10 x  y , m4  5 x  3 y
2
1
3
4
D
P
6. Use the diagram below to answer the following.
a. Name three collinear points.
b. Name three noncollinear points.
c. Name four coplanar points.
d. Name four noncoplanar points.
 
e. Find AB  GB .

f. Find DE  CD .
 
g. Find BD  CE
 
h. BA  BD
i. R CE
j. R  P
R
G
C
D
B
E
A
F
7. In the diagram below MN  NP , m1  3 x  8 y, m2  3 x  2 y , and m3  6 x  2 y . Find
m3.
M
2
1
N
3
P
8. In the diagram, m1 = 6x + 21 and m2 = 10x – 25. Are the lines perpendicular? Give an
explanation for your answer.
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2