Download 2.8

Lesson 2.8
Vertical Angles
Objective:
After studying this lesson you will be able
to recognize opposite rays and vertical
angles.
AB and AC are opposite rays
B
A
C
Definition Two collinear rays that have a common
endpoint and extend in different
directions are called opposite rays.
Are all pairs of rays called opposite rays?
K
J
O
B
M
A
Key questions:
Are they on the
same line?
D
C
Do the rays share
the same endpoint?
Vertical Angles
Whenever two lines intersect, two pairs
of vertical angles are formed.
4
1
2
3
1 and 3
2 and 4
are vertical angles
Definition
Two angles are vertical angles if the
rays forming the sides of one and
the rays forming the sides of the
other are opposite rays
Are angle 3 and angle 2
vertical angles?
4
1
2
3
How do vertical angles
compare in size?
Theorem 18 Vertical angles are congruent
92
Find the missing angles
Given:
Prove:
5
Diagram as shown
5  7
Statements
Reasons
6
7
Given:
2  3
1
2
3
Prove:
1  3
Statements
Reasons
Given: O is complementary to 2
O
J is complementary to 1
Prove: O  J
H
J
Statements
Reasons
2
1 K
M
Given:
Find:
m4  2 x  5
m5  x  30
m4
4
5
Summary…
Explain what opposite rays are and
how they relate to vertical angles?
Homework
Lesson 2.8 Worksheet