1. W ARM U P If Bessie is a cow then she is a mammal. State the truth value for each. Converse: If Bessie is a mammal then she is a cow. False: Dog Inverse: If Bessie is not a cow then she is not a mammal. False. Cat Contra positive: If Bessie is not a mammal then she is not a cow. True.

2. S ECTION 6 (P AGE 15) Geometric Proofs

3. J USTIFICATION Write a justification for each step, given that < A and < B are complementary and < A < C. A B C

4. J USTIFICATION Write a justification for each step, given that B is the midpoint of AC and

5. T HEOREM Any statement that you can prove.

6. Theorem HypothesisConclusion Linear Pair Theorem: If two angles form a linear pair then they are supplementary < A and < B form a linear pair <A and <B are supplementary Congruent Supplement Theorem: If 2 angles are supplementary to the same angle then the 2 angles are congruent <1 and < 2 are supplemenatary <2 and <3 are supplemenatry

7. T WO -C OLUMN P ROOF You list the steps of the proof on the left column and the matching reason in the right column.

8. Given: < 1 and < 2 form a linear pair Prove: < 1 and < 2 are supplementary StatementsReasons < 1 and < 2 form a linear pair form a lineDefinition of a linear pair m<ABC = 180°Definition of a straight line Angle Addition Postulate Substitution (Steps: _______) < 1 and < 2 are supplementary A BC 1 2

9. Given: < 1 and < 2 are supplementary and < 2 and < 3 are supplementary Prove: < 1 < 3 StatementsReasons Given m < 1 + m < 2 = 180° m < 2 + m < 3 = 180° Substitution (Step 2) m < 2 = m < 2 m < 1 = m < 3 1 2 3

10. Theorem HypothesisConclusion Right Angle Theorem: All right angles are congruent. < A and < B are right angles Congruent Complements Theorem: If two angles are complementary to the same angle then the two angles are congruent < 1 and < 2 are complementary <2 and < 3 are complementary

11. Given: < 1 and < 2 are right angles Prove: < 1 < 2 StatementsReasons m < 1 = 90° m < 2 = 90° m <1 = m < 2 < 1 < 2 1 2

12. Given: < 1 and < 2 are complementary and < 2 and < 3 are complementary Prove: < 1 < 3 StatementsReasons Given m < 1 + m < 2 = 90° m < 2 + m < 3 = 90° m < 2 = m < 2 1 2 3