1. WARM UP Make a list of things you can and cannot assume from the diagram.

2. 1.4 Beginning Proofs Two-column Proofs and Theorems Theorem: a mathematical statement that can be proven. Postulate:Mathematical statement accepted as true.

3. Theorem Procedures to follow: 1.We present a theorem or theorems 2.We prove the theorem(s) using postulates definitions and other theorems. We shall omit the proofs of certain theorems, even though all have proofs

4. 3. We use the theorems to help prove sample problems. 4.You 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! Theorem Procedures to follow:

5. Theorem 1 If two angles are right angles, then they are congruent. Given: <A is a right angle <B is a right angle Prove: <A is congruent to <B A B

6. Theorem 1 - Proof: StatementReason 1. <A is right angleGiven 2. m<A = 90  If right angle then 90  3. <B is right angleGiven 4. m<B = 90  Same as #2 5. <A congruent <BIf two angles have the same measure, then they are congruent. Steps 2&4

7. Theorem 2 If two angles are straight angles, then they are congruent. Given: <ABC is a straight angle <DEF is a straight angle Prove: <ABC is congruent to <DEF A BC D EF

8. StatementReason 1.<ABC is straight angleGiven 2. m<ABC = 180˚If angle is straight then m=180˚ 3. <DEF is straight angleGiven 4. m<DEF = 180˚  Same as #2 5. <ABC congruent <DEFIf two angles have the same measure, then they are congruent. Steps 2&4 Theorem 2 - Proof: