1. Chapter 2
Reasoning and Proof

2. 2.8 Proving Angle Relationships
Angle Addition Postulate – If S is in the interior of ∠𝑃𝑄𝑅, then 𝑚∠𝑃𝑄𝑆+𝑚∠𝑆𝑄𝑅=𝑚∠𝑃𝑄𝑅.

3. Theorems: If 2 angles are a linear pair, then they are supplementary.
If noncommon sides of adjacent angles form a right angle, then the adjacent angles are complementary.
Angles supplementary to the same angle are congruent.
Angles complementary to the same angle are congruent.

4. Theorems: Vertical angles are congruent.
Perpendicular lines intersect to form 4 right angles.
All right angles are congruent.
Perpendicular lines form 4 congruent adjacent angles.
If 2 angles are congruent and supplementary, then they are right angles.
If 2 angles form a linear pair, then they are right angles.

5. Example 1.

6. Example 2.

7. Example 3.

8. Example
Determine whether the following statements are always, sometimes, or never true. Explain.
5. Two angles that are nonadjacent are vertical.
6. Two acute angles that are congruent are complementary to the same angle.

9. Example
Write a two-column proof.