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Vertical Angles. Lesson 2.8. 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. Y. V. U.

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vertical angles

Vertical Angles

Lesson 2.8

slide2

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.

slide3

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.

slide5

Definition: 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

B

A

2

1

4

C

D

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

slide6

Theorem 18:Vertical angles are congruent.

6

7

5

Given: diagram

Prove <5 congruent to <7

Hint: use supplementary angles

slide8

1

Given: <2 congruent to <3

Prove: <1 congruent to <3

2

3

  • Given
  • Vertical angles are .
  • If s are  to the same , they are  . (Transitive Property)
  • 2  3
  • 1  2
  • 1 3
slide9

5

4

6

m 4 = 2x +5

m 5 = x + 30

Find the m4 and m6

slide10

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