1. Proving Angle Relationships
Chapter 2 Section 8

2. Angle Addition Postulate

3. Using the Angle Addition Postulate1
EXAMPLE
Using the Angle Addition Postulate 75

5. Find the measure of each numbered angle and name the theorem that justifies your work.
They are a linear pair, so they
will add to 180. Solve for x.
All angles add to 180. Solve for x.
Angles 1 and 2 add to 90.
Angles 11 and 13 add to 180.

6. Properties of Congruent Angles
Reflexive Property
∠ A ≅ ∠ A
Symmetric Property
If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A
Transitive Property
If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

7. Theorem 2.4:Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

8. Theorem 2.5:Congruent Complements Theorem
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

9. Theorem 2.8 Vertical Angles Theorem
Vertical angles are congruent. 2 3 1 4
∠1 ≅ ∠3; ∠2 ≅ ∠4

10. Example – Using Vertical Angles Theorem
Find the value of x 4x
3x + 35
What is each angle measure?
Set 4x = 3x + 35
Solve for x

11. Right Angle Theorems

12. More right angle theorems

13. Have a great day! 