Lesson 2.8 Vertical Angles Objective: After studying this lesson you will be able to recognize opposite rays and vertical angles.

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Presentation transcript:

Lesson 2.8 Vertical Angles Objective: After studying this lesson you will be able to recognize opposite rays and vertical angles.

A Definition Two collinear rays that have a common endpoint and extend in different directions are called opposite rays. B C

Are all pairs of rays called opposite rays? OM J K A B C D Key questions: Are they on the same line? Do the rays share the same endpoint?

Vertical Angles Whenever two lines intersect, two pairs of vertical angles are formed DefinitionTwo 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? How do vertical angles compare in size? Theorem 18 Vertical angles are congruent 92Find the missing angles

Diagram as shown Given: Prove: Statements Reasons 5 7 6

Statements Reasons Given: Prove: 1 2 3

Statements Reasons Given: Prove: 1 2 O M J H K

Given: Find: 4 5

Lesson 2.8 Worksheet Homework Summary… Explain what opposite rays are and how they relate to vertical angles?