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

Objectives To prove and apply theorems about angles.

Vocabulary Theorem Proof

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

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

Prove Theorem 2-1

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

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

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.

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.

Theorem 2-4: All right angles are congruent.

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