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Lesson 2-5 1 Conditional Statements

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Lesson 2-5 2 Conditional Statement Definition:A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Example:If your feet smell and your nose runs, then you're built upside down. Continued……

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Lesson 2-5 3 Conditional Statement - continued Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.) The conclusion is the part of an if-then statement that follows “then” (when written in if-then form.) The hypothesis is the given information, or the condition. The conclusion is the result of the given information.

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Lesson 2-5 4 Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Writing Conditional Statements Hint: Turn the subject into the hypothesis. Example 1:Vertical angles are congruent.can be written as... If two angles are vertical, then they are congruent. Conditional Statement: Example 2:Seals swim. can be written as... Conditional Statement: If an animal is a seal, then it swims.

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Lesson 2-5 5 If …Then vs. Implies Two angles are vertical implies they are congruent. Another way of writing an if-then statement is using the word implies. If two angles are vertical, then they are congruent.

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Lesson 2-5 6 Conditional Statements can be true or false: A conditional statement is false only when the hypothesis is true, but the conclusion is false. A counterexample is an example used to show that a statement is not always true and therefore false. If you live in N.C., then you live in Raleigh.Statement: Counterexample:I live in NC, BUT I live in Kernersville. Is there a counterexample? Therefore ( ) the statement is false. Yes !!!

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Lesson 2-5 7 Forms of Conditional Statements Converse: Switch the hypothesis and conclusion If two angles are vertical, then they are congruent. If two angles are congruent, then they are vertical. Continued…..

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Lesson 2-5 8 Forms of Conditional Statements Inverse: State the opposite of both the hypothesis and conclusion. If two angles are vertical, then they are congruent. If two angles are not vertical, then they are not congruent.

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Lesson 2-5 9 Forms of Conditional Statements Contrapositive: Switch the hypothesis and conclusion and state their opposites. If two angles are vertical, then they are congruent. If two angles are not congruent, then they are not vertical.

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Lesson 2-5 10 Forms of Conditional Statements Contrapositives are logically equivalent to the original conditional statement.

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Lesson 2-5 11 Biconditional When a conditional statement and its converse are both true, the two statements may be combined. Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90 . Converse: If an angle measures 90 , then it is a right angle. Biconditional: An angle is right if and only if it measures 90 .

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Lesson 2-5 12 Law of Detachment Given: a true conditional statement and the hypothesis occurs Conclusion: the conclusion will also occur

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Lesson 2-5 13 Law of Detachment - Example Given: If three points are collinear, then the points are all on one line. E, F, and G are collinear. Conclusion: E, F, and G are all on one line. Example 1: Given: If I find $20 in the street, then I’ll take you to the movies. On October 10 I found $20 in the street. Conclusion: I will take you to the movies. Example 2:

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Lesson 2-5 14 Law of Syllogism Given: Two true conditional statements and the conclusion of the first is the hypothesis of the second. Conclusion: If the hypothesis of the first occurs, then the conclusion of the second will also occur.

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Lesson 2-5 15 Law of Syllogism - Example If it rains today, then we will not see our friends. Example: If it rains today, then we will not have a picnic. If we do not have a picnic, then we will not see our friends. Conclusion: Given:

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