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.

3. Theorem Procedures to follow: 1.We present a theorem or theorems 2.We prove the theorem(s) 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! http://player.discoveryeducation.com/index.cfm?g uidAssetId=30453D1E-A4ED-453D-AF6E- A891E3C3E77E&blnFromSearch=1&productco de=US

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. Set Up: Proof Statements 1.<A is right < 2.m<A = 90  3.<B is right < 4.m<B = 90  5.<A congruent <B Reasons 1.Given 2.If right < then 90  3.Given 4.Same as #2 5.If 2 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. Proof Statements 1.<ABC is straight < 2.m<ABC = 180˚ 3.<DEF is straight < 4.m<DEF = 180˚ 5.<ABC congruent <DEF Reasons 1.Given 2.If < is straight then m=180˚ 3.Given 4.Same as #2 5.If 2 angles have the same measure, then they are congruent. Steps 2&4