1. CONDITIONAL STATEMENTS Section 2-1

2. Objectives  To recognize conditional statements.  To write converses of conditional statements.

3. Have you ever heard a person say: If you are not completely satisfied, then your money will be refunded? This is an if-then statement called a ______________.

4. Every conditional statement has two parts. The part following the if is the _____________. The part following the then is the ___________.

5. Example 1:Identify the Hypothesis and the Conclusion If today is the first day of fall, then the month is September. Hypothesis: Conclusion:

6. Example 2:Identify the Hypothesis and the Conclusion If you want to be fit, then get plenty of exercise. Hypothesis: Conclusion:

7. Converse To find the Converse of a Conditional -Switch the Hypothesis and Conclusions around, But you keep the “IF” and “Then” where they are.

8. Write the converse of the conditional statement. Example : If two lines are not parallel and do not intersect, then they are skew lines.

9. Write the converse of the conditional statement Example : If you eat your vegetables, then you grow.

10. Write the converse of the conditional statement Example: If a triangle is a right triangle, then it has a 90 degree angle.

11. Truth Values (true or false?) Converses are NOT ALWAYS TRUE. Write the converse of the conditional AND determine it’s truth value. If a figure is a square, then it has four sides.

12. Truth Values (true or false?) Example: Write the converse of the conditional AND determine it’s truth value. If two lines do not intersect, then they are parallel.

13. Truth Values (true or false?) Example: Write the converse of the conditional AND determine it’s truth value. If x = 2, then |x| = 2.

14. BICONDITIONALS AND DEFINITIONS Section 2-2

15. Objectives  To write biconditionals.  To recognize good definitions.

16. Objective A ______________ is the combination of a conditional statement and its converse. A biconditional (statement) contains the words “___________________.”

17. Consider the true conditional statement. Write its converse. If the converse is also true, combine the statements as a biconditional. 1. Conditional: If two angles have the same measure, then the angles are congruent.

18. Consider the true conditional statement. Write its converse. If the converse is also true, combine the statements as a biconditional. 2. Conditional: If three points are collinear, then they lie on the same line.

19. Recognizing a Good Definition - Use the examples to identify the figures above that are polyglobs. Write a definition of a polyglob by describing what a polyglob is. See Page 76

20. Show that the definition is reversible. Then write it as a true biconditional. 1. Definition: Perpendicular lines are two lines that intersect to form right angles.

21. Show that the definition is reversible. Then write it as a true biconditional. 2. Definition: A right angle is an angle whose measure is 90 (degrees).

22. Is the given statement a good definition? Explain. 1. An airplane is a vehicle that flies. 2. A triangle has sharp corners. 3. A square is a figure with four right angles.

23. DEDUCTIVE REASONING “LAWS OF DETACHMENT/SYLLOGISM” Section 2-3

24. Classwork Page 71 12 – 26 even, 54 – 58 Page 78 1 – 12, 27 – 35, 41 – 43 Page 84 1 – 15 odd Page 102 44 - 51