1. Review Complete the chart: pq Conditional p  q Converse _  _ TT TF FT FF

2. Inverse and Contrapositive Geometry Unit 9, Day 6 Mr. Zampetti

3. Objective Write the inverse and contrapositive of if-then statements

4. Reminder! Conditional: p  q. The phrase after the word “if” is the hypothesis. (p) The phrase after the word “then” is the conclusion. (q)

5. Definition Inverse – Negating both the hypothesis and conclusion of the conditional. Ex. Conditional: If two angles have the same measure, then they are congruent. Inverse: If two angles do not have the same measure, then they are not congruent.

6. Conditional to Inverse Conditional: p  q Inverse: ~p  ~q Conditional: ~p  q Inverse : p  ~q Conditional: ~q  ~p Inverse : q  p

7. Truth Table for Inverse pq~p~q Conditional p  q Inverse ~p  ~q TT TF FT FF

8. Definition Contrapositive – Negating AND exchanging both the hypothesis and conclusion Ex. Conditional: If two angles have the same measure, then they are congruent. Contrapositive: If two angles are not congruent then they do not have the same measure.

9. Conditional to Contrapositive Conditional: p  q Contrapositive: ~q  ~p Conditional: ~p  q Contrapositive: ~q  p Conditional: ~q  ~p Contrapositive: p  q

10. Truth Table for Contrapositive pq~p~q Conditional p  q C ontrapositive ~q  ~p TT TF FT FF

11. Practice Write the converse, inverse, and contrapositive of the following conditional statement: If two angles equal 90°, then they are complementary.

12. Answer Converse: If two angles are complementary, then they equal 90° Inverse: If two angle do not equal 90° then they are not complementary Contrapositive: If two angles are not complementary then they do not equal 90°

13. Homework Work Packet: Inverse and Contrapositive