1. Warm Up: 1)Given: AB bisects <CAD, AE bisects <BAD, and AC bisects <MAD. If m<CAD = 48, find: a. m<MAB b. m<BAE A D E B C M 12° 24° 48° 72° 12°

2. Proving Theorems Reasons Used in Proofs –Given Information –Definitions –Postulates (These include properties from Algebra) –Theorems that have already been proved

3. StepsReasons Given 1. 2. 3. 4. Addition Property of Equality Segment Addition Postulate Substitution Property Given: RT and PQ intersect at S so that RS = PS and ST = SQ Prove: RT = PQ R Q P T S RS = PS; ST = SQ RS + ST = PS + SQ RS + ST = RT; PS + SQ = PQ RT = PQ

4. StepsReasons Given 1. 2. 3. 4. Angle Addition Postulate Substitution Property Reflexive Property Given: Prove: O D C B A 3 21 5. Subtraction Property of Equality

5. Midpoint Theorem If M is the midpoint of AB, then AM = 1/2AB and MB = 1/2AB ABM Given: M is the midpoint of AB k Prove: AM = 1/2AB; MB = 1/2AB StatementsReasons 1. k 2. k3. 4. 5. k 6. M is the midpoint of AB Given AM = MBDefinition of a midpoint AM + MB = ABSegment Addition Postulate AM + AM = AB, or 2AM = ABSubstitution Property AM = 1/2ABDivision Prop. Of Equality MB = 1/2ABSubstitution Property