SWLT: Write proofs using geometric theorems and use properties of special pairs of angles.

In a proof, you make one statement at a time, until you reach your conclusion. Because the Statements made are based on facts, you are using deductive reasoning. Usually the 1 st statement- and-reason pair written is the given information Statements Reasons

1. M is a Midpoint of AB 2. AM ≅ MB 3. AM = MB 4. AM + MB = AB 5. AM + AM = AB 6. 2  AM = AB 1. Given 2. Definition of Midpoint 3. Def. of Congruent Segments 4. Segment Add. Postulate 5. Substitution Prop. Of Eq. 6. Distributive Prop. Of Eq. A BM Statements Reasons

1. B is a Midpoint of AC. C is a Midpoint of BD 2. AB ≅ BC 3. BC ≅ CD 4. AB ≅ CD 5. AB = CD 1. Given 2. Definition of Midpoint 3. Definition of Midpoint 4. Transitive Property 5. Def. of Congruence A CB Statements Reasons D (Draw two Separate Segments)

Congruent Complements Theorem If two angles are complementary to the same angle, then they are congruent If m  1 + m  2 = 90° and m  2 + m  3 = 90°, then  1 ≅  3 Congruent Supplements Theorem If two angles are supplementary to the same angle, then they are congruent If m  4 + m  5 = 180° and m  5 + m  6 = 180°, then  4 ≅ 

1.  1 &  2 are supplements,  3 &  2 are supplements. 2. m  1 + m  2 = 180° 3. m  3 + m  2 = 180° 4. m  1 + m  2 = m  3 + m  2 5. m  1 = m  3 6. m  1 ≅ m  3 1. Given 2. Def. of Supplementary Angles 3. Def. of Supplementary Angles 4. Transitive Property 5. Subtraction Property 6. Def. of Congruence Statements Reasons (Congruence of Supplements Proof)