Analyze Conditional Statements

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Presentation transcript:

Analyze Conditional Statements Lesson 2.2 Analyze Conditional Statements

Objective Write definitions as conditional statements

Standard 3.0 – Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.

Conditional Statement A logical statement that has two parts, a hypothesis and a conclusion If-Then form If (hypothesis), then (conclusion)

Example If it is raining, then there are clouds in the sky. hypothesis Conclusion

Example Rewrite the conditional statement in if-then form. All birds have feathers Two angles are supplementary if they are a linear pair

Practice All 90° angles are right angles. 2x + 7 = 1 because x = -3 Tourists at the Alamo are in Texas

Negation Opposite of a statement To negate something

Example The ball is red. The ball is not red

The cat is not black. The cat is black

3 negations of conditional statement Converse – exchange hypothesis and conclusion Inverse – negate both hypothesis and conclusion Contrapositive – first write converse and then negate hypothesis and conclusion

Example Conditional Statement True or False If m∠A=99°, then ∠A is obtuse Converse If ∠A is obtuse, then m∠A=99° Inverse If m∠A≠99°, then ∠A is not obtuse Contrapositive If ∠A is not obtuse, then ∠A≠99°

Homework p.83 #1, 2, 4, 5, 9

Example Write If-Then, Converse, Inverse, and Contrapositive of “Guitar Players are Musicians”

Perpendicular Lines

Example

Biconditional Statement Conditional statement and its converse are both true “If and only if”

Example Definition If two lines intersect to form a right angle, then they are perpendicular Converse: If two lines are perpendicular, then they intersect to form a right angle. Biconditional: Two lines are perpendicular, if and only if, they intersect to form a right angle

Homework p.83 #16, 17, 18, 33-39 odd, 42, 45, 47, 49