OBJECTIVES:1) TO IDENTIFY ANGLE PAIRS

2) TO PROVE AND APPLY THEOREMS ABOUT ANGLES

2-5 Proving Angles Congruent

M11.B.2 2.5.11.C

VocabularyVertical Angles – two angles whose sides form

two pairs of opposite rays 1 3 4 2

Adjacent Angles – two coplanar angles with a common side, a common vertex, and no common interior points

1 2

VocabularyComplementary Angles – two angles whose

measures have sum 90°. Each angle is called the complement of the other.

A 60 B 30

Supplementary Angles – two angles whose

measures have sum 180°. Each angle is called the supplement of the other.

3 4 75 105

Example: Identifying Angle Pairs

• Name all pairs of anglesa) Vertical:b) Supplementary:c) Complementary:

1

2 34

Example: Identify Angle Pairs

Complementary:Supplementary:Vertical:

2

1 3

5 4

Assumptions from Diagram

**Things you can conclude from a diagram:

1) Adjacent angles2) Adjacent supplementary angles3) Vertical angles

Can NOT Assume: (Unless Marked)

**Things you cannot conclude from a diagram without markings

1) Angles or segments are congruent2) An angle is a right angle3) Lines are parallel or perpendicular

Example: Making Conclusions from a Diagram

True or False1) < 3 is a right angle2) < 1 and < 5 are adjacent3) < 3 = < 5

12

34

5

Vertical Angle Theorem

Vertical angles are congruent.

Example: Find the value of x

2x - 3

4x - 10