Beginning Proofs

Lesson 1.4

Two column proofs and theorems

Theorem: A mathematical statement that can be proven.We prove theorem(s)

We shall omit the proofs of certain theorems, even though all have proofs

We use theorems to help prove sample problemsYou are then given the challenge of using the theorems to prove homework problems. Theorems will save you much time if you learn them and then use them!

You use theorems to prove others,

Do not use proffs of theorems as a guide.

Use sample problems as a guide.

You use deductive reasoning to prove theorems. (Basically you create a chain of logical steps that move from the hypothesis to the concusion of the conjecture you are proving

Theorem 1: If two angles are right angles, then they are congruent

Given: <A is a right <

<B is a right <

Prove: <A <B

Proof:Statements Reasons

1. <A is a right angle 1. Given

2. M<A = 90 2. Right angles = 90

3. <B is a right angle 3. Given

4. M<B = 90 4. Right angles = 90

5. <A <B 5. Two angles of the same

measure are congruent

Theorem 2: If two angles are straight angles, then they are congruent.

Given: Diagram

Prove: <ABC <FBD

Given: <ABC = 115

<XYZ = 115

Prove: <ABC <XYZ

Statements Reasons

1. <ABC = 115 1. Given

2. <XYZ = 115 2. Given

3. <ABC <XYZ 3. Def of angles

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