1. Warm Up Given: Diagram as shown Prove: <1 congruent <3
Hint: Think of Supplementary Angles!
<ABC is a straight < 1. Assumed
<1 is supp to < If 2 adjacent <s form
a straight <, they are supp
3. <DBE is a straight < 3. Same as 1
4. <2 is supp to <3 4. Same as 2
5. <1 congruent to <3 5. Supplements of the
same < are congruent

2. 2.8 Vertical Angles

3. 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.

4. B A C D
Ray BA and Ray CD are not opposite rays. X Y V U
Ray UV and Ray XY are not opposite rays. NO common end point.

5. Vertical Angles: when ever two lines intersect, two pairs of vertical angles are formed.
You can assume Vertical Angles!

6. 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. 3 E A B 2 1 4 C D
<1 &<2; <3 & <4 are vertical angles.

7. T18: Vertical angles are congruent.6 7 5
Given: diagram
Prove <5 congruent to <7
Hint: use supplementary angles

8. 2.4 problem
Therefore < <7

9. Given: <2 congruent to <3
Prove: <1 congruent to <3 1 2 3

11. 5 4 6
m<4 = 2x +5
m<5 = x + 30
Find the m<4 and m<6

12. 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 =
= 125