1. 2-5 Proving angles congruent

2. Vertical angles
Two angles whose sides are opposite rays 1 3 4 2

3. Adjacent angles
Two coplanar angles with a common side, a common vertex, and no common interior points 3 4 1 2

4. Complementary angles Two angles that ADD up to 90˚
Each angle is called the complement of the other
50° 1 A 2
40° B

5. Supplementary Angles Two angles that ADD up to 180°
Each angle is called the supplement
of the other
105°
75° 3 4

6. Examples! 1. Identify Angle Pairs Complementary Supplementary Vertical
Adjacent 1 2 3 4 5

7. 2. What can you tell from the picture?
About ∠1 and ∠2?
What type of angles are ∠2 and ∠3?
What type of angles are ∠4 and ∠5?
What type of angles are ∠1 and ∠4? 3 2 1 5 4

8. Vertical Angles Theorem (2-1)
Vertical angles are congruent (≅)
∠1 ≅ ∠2 and ∠3 ≅ ∠4 1 2 3 4

9. Using the vertical angles theorem
Find the value of x.
Find the value of each angle. 4x
(3x + 35)

10. Congruent Supplements Theorem (2-2)
If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
∠1 and ∠2 are supplementary
(∠2 is a supplement of ∠1)
∠1 and ∠3 are supplementary
(∠3 is a supplement of ∠1)
So ∠2 ≅ ∠3 1 2 3

11. Congruent Complements Theorem (2-3)
If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.
Theorem 2-4: All right angles are congruent.
Theorem 2-5: If two angles are congruent and supplementary, then each is a right angle.

12. Ticket Out the door