Presentation on theme: " Conditional Statement A statement that can be written in If-Then form If-Then Statement Statement written in the form If p, then q. Hypothesis."— Presentation transcript:
Conditional Statement A statement that can be written in If-Then form If-Then Statement Statement written in the form If p, then q. Hypothesis The portion right after the If Conclusion The portion right after the Then
Identify the hypothesis and conclusion in each statement If 2x+6=10, then x=2 If 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
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
Converse Exchanging the hypothesis and conclusion of the conditional Inverse Negating both the hypothesis and conclusion of the conditional Contrapositive Negating both the hypotheses and conclusion of the converse statement If 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.
Counterexample Shows that a conditional statement is false where the hypothesis is true and the conclusion is false
Show the conditional is false by finding a counterexample If 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.
Counterexample Shows that a conditional statement is false where the hypothesis is true and the conclusion is false Biconditional Combination of a conditional and its converse p if and only if q
Write each biconditional as a conditional and its converse Two 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.