Chapter Two:Reasoning and Proof

Section 2-5:Proving Angles Congruent

Objectives

To prove and apply theorems about angles.

Vocabulary

TheoremProof

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 2-1Given: 1 and 2 are vertical angles

Prove: 1 2

Statements: Reasons:

1) 1 3 180 1)______________

2 3 180

2) 1 3 2 3 2)______________

3)____________________ 3) Subtra

m m

m m

m m m m

ction Property of Equality

4)____________________ 4) Definition of Congruence

Proof

A proof is a convincing argument that uses deductive reasoning.

There are several types of proofs which include:Paragraph proofsColumn 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.