1. Analyze Conditional Statements
Lesson 2.2
Analyze Conditional Statements

2. Objective
Write definitions as conditional statements

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

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

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

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

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

8. Negation
Opposite of a statement
To negate something

9. Example
The ball is red.
The ball is not red

10. The cat is not black.
The cat is black

11. 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

12. 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°

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

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

15. Perpendicular Lines

16. Example

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

18. 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

19. Homework
p.83 #16, 17, 18, odd, 42, 45, 47, 49