Warm Up Given: Diagram as shown Prove:

Warm UpWarm UpGiven: Diagram as shownProve: <1 congruent <3

Hint: Think of Supplementary Angles!

3. <DBE is a straight < 3. Same as 14. <2 is supp to <3 4. Same as 25. <1 congruent to <3 5. Supplements of the

same < are congruent

2.8 Vertical Angles2.8 Vertical Angles

http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431584.html

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.

V UX Y

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 BE

D C

1 24

3

<1 &<2; <3 & <4 are vertical angles.

T18: Vertical angles are congruent.

5

67

Given: diagram

Prove <5 congruent to <7

Hint: use supplementary angles

2.4 problem2.4 problem

Therefore <5 <7

Given: <2 congruent to <3

Prove: <1 congruent to <3

123

45

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