1. Chapter Two: Reasoning and Proof Section 2-5: Proving Angles Congruent

2. Objectives To prove and apply theorems about angles.

3. Vocabulary Theorem Proof

4. Theorem A theorem is a conjecture that is proven. We use proofs to show that theorems are true.

5. Theorem 2-1: “Vertical Angles Theorem” Vertical Angles are Congruent.

6. Prove Theorem 2-1

7. Proof A proof is a convincing argument that uses deductive reasoning. There are several types of proofs which include: Paragraph proofs Column proofs

8. Using the Vertical Angles Theorem Solve for the values of x:

9. Theorem 2-2: “Congruent Supplements Theorem” If two angles are supplements of the same angle (or of congruent angles) then they are congruent to each other.

10. Theorem 2-3: “Congruent Supplements Theorem” If two angles are complements of the same angle (or of congruent angles) then they are congruent to each other.

11. Theorem 2-4: All right angles are congruent.

12. Theorem 2-5: If two angles are congruent and supplementary, then each is a right angle.