Presentation on theme: "SWBAT: analyze statements in the If-Then form. ()"— Presentation transcript:
1 SWBAT: analyze statements in the If-Then form. ()
2 If-Then Statements Conditional Statement If-Then Statement Hypothesis A statement that can be written in If-Then formIf-Then StatementStatement written in the form If p, then q.HypothesisThe portion right after the IfConclusionThe portion right after the Then
3 If-Then StatementsIdentify the hypothesis and conclusion in each statementIf 2x+6=10, then x=2If you are a teenager, then you are at lease 13 years old.“If a man hasn’t discovered something that he will die for, he isn’t fit to live”Martin Luther King, Jr.“If somebody throws a brick at me, I can catch it and throw it back.”Harry S Truman
4 If-then Statements Write each statement in if-then form. Get a free visit with a one-year fitness plan.Math teachers love to solve problems.Adjacent angles have a common side.Vertical angles are congruent.“We’re half the people; we should be half the congress”Jeanette Rankin, former US Congresswoman, calling for more women in office“A great work is made out of a combination of obedience and liberty.”Nadia Boulanger, orchestra conductor and musical mentor“A problem well stated is a problem half solved”Charles F Kettering, inventor
5 Related Conditionals Converse Inverse Contrapositive Exchanging the hypothesis and conclusion of the conditionalInverseNegating both the hypothesis and conclusion of the conditionalContrapositiveNegating both the hypotheses and conclusion of the converse statementIf two angles have the same measure, then they are congruent.If two angles are congruent, then they have the same measure.If two angles do not have the same measure, then they are not congruent.If two angles are not congruent, then they do not have the same measure.
6 Related Conditionals Counterexample Shows that a conditional statement is false where the hypothesis is true and the conclusion is false
7 Related ConditionalsShow the conditional is false by finding a counterexampleIf it is February, then there are only 28 days in a month.If the name of a state contains the word New, then the state boarders an ocean.If it is not a weekday, then it is Saturday.Odd integers less than 10 are prime.If you play a sport where you hit a ball, then you play baseball.
8 Related Conditionals Counterexample Biconditional Shows that a conditional statement is false where the hypothesis is true and the conclusion is falseBiconditionalCombination of a conditional and its conversep if and only if q
9 Related ConditionalsWrite each biconditional as a conditional and its converseTwo angle measures are complements if and only if their sum is 90.Two angles are congruent if and only if they have the same measure.A line is a segment bisector iff it intersects the segment at its midpoint.