1. 2.6 What you should learn Why you should learn it
PROVING STATEMENTS ABOUT ANGLES
What you should learn
GOAL 1
Justify statements about congruent angles.
GOAL 2
Prove properties about special pairs of angles
Why you should learn it
Properties of special pairs of angles help you determine angles in real-life applications, such as design work.

2. 2.6 PROVING STATEMENTS ABOUT ANGLES 1 GOAL
PROPERTIES OF CONGRUENT ANGLES
VOCABULARY
PROPERTIES OF
ANGLE CONGRUENCE
Reflexive
Symmetric
Transitive
EXAMPLE 1

3. Extra Example 1 Given: Prove: A C B 1 2 3 4 Statements Reasons 1. 1.
Given
Transitive Prop. of 
Given
Transitive Prop. of 
EXAMPLE 2

4. Extra Example 2 Given: Prove: 1 2 4 3 Statements Reasons 1. 1. Given
Transitive Prop. of 
Def. of 
Given
Subs. Prop. of =

5. All right angles are congruent.
CONGRUENCE THEOREM
All right angles are congruent.
EXAMPLE 3

6. Extra Example 3 Given: Prove: A B C D Statements Reasons 1. 1. Given
Transitive Prop. of 

7. Checkpoint Given: Prove: A B C D E F Statements Reasons 1. 1. Given
Transitive Prop. of 

8. 2.6 PROVING STATEMENTS ABOUT ANGLES 2 GOAL USING CONGRUENCE OF ANGLES
CONGRUENT SUPPLEMENTS THEOREM
Two angles supplementary to the same angle (or congruent angles) are congruent
CONGRUENT COMPLEMENTS THEOREM
Two angles complementary to the same angle (or congruent angles) are congruent
In proofs, these may be abbreviated as  Supp. Thm. and  Comp. Thm.
EXAMPLE 4

9. Extra Example 4 Given: Prove: 1 2 3 4 Statements Reasons 1. 1. Given
Transitive Prop. of =
 Complements Thm.

10. If two angles form a linear pair, then they are supplementary.
Checkpoint
1. In a diagram, are supplementary and
are supplementary. Explain how to show that
Using the definition of supplementary angles, So
by the transitive property of
equality. So by the subtraction property of
equality. Therefore, by the definition of congruent angles.
LINEAR PAIR POSTULATE
EXAMPLE 5
If two angles form a linear pair, then they are supplementary.

11. Extra Example 5 In the diagram is right. Explain how to show A B C D EF 1 2 3 4
Using the substitution property, you know that
by the Angle Addition Postulate. The diagram shows that
Substitute 150° for to
show
VERTICAL ANGLES THEOREM
EXAMPLE 6
Vertical angles are congruent.

12. Extra Example 6 Given: are a linear pair, are a linear pair. Prove: 12 3
Statements Reasons
Given
Linear Pair Post.
 Supplements Thm.

13. Checkpoint 1. Find the measures of the angles in the diagram given
and are complementary and 1 2
78° 3 4

14. QUESTIONS?