Download 2.8 Vertical Angles

Warm Up
Given: Diagram as shown
Prove: <1 congruent <3
Hint: Think of
Supplementary Angles!
1. <ABC is a straight <
2. <1 is supp to < 2
3. <DBE is a straight <
4. <2 is supp to <3
5. <1 congruent to <3
1. Assumed
2. If 2 adjacent <s form
a straight <, they are
supp
3. Same as 1
4. Same as 2
5. Supplements of the
same < are congruent
2.8 Vertical Angles
http://www.phschool.com/atschool
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Opposite Rays:
Two collinear rays that have a
common endpoint and extend in
different directions
B
A
C
Ray AB and ray AC are opposite rays.
B
A
C
D
Ray BA and Ray CD are not
opposite rays.
X
V
Y
U
Ray UV and Ray XY are not opposite
rays. NO common end point.
Vertical Angles: when ever two
lines intersect, two pairs of
vertical angles are formed.
You can assume Vertical Angles!
Def: Two angles are vertical
angles if the rays forming the
sides of one angle and the rays
forming the sides of the other are
opposite rays.
A
3
1
B
E
2
4
C
D
<1 &<2; <3 & <4 are vertical angles.
T18: Vertical angles are congruent.
6
5
7
Given: diagram
Prove <5 congruent to <7
Hint: use  supplementary angles
2.4 problem
Therefore <5

<7
Given: <2 congruent to <3
Prove: <1 congruent to <3
1
2
3
4
5
6
m<4 = 2x +5
m<5 = x + 30
Find the m<4 and m<6
Vertical angles are congruent so just set them
equal to each other and solve for x.
REMEMBER to plug x back in to find the angle.
The measure of <6 = 180-55
= 125