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

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Presentation transcript:

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

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

Objective Write the inverse and contrapositive of if-then statements

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

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.

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

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

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.

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

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

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

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°

Homework Work Packet: Inverse and Contrapositive