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6. Contents Lesson 2-1Inductive Reasoning and Conjecture Lesson 2-2Logic Lesson 2-3Conditional Statements Lesson 2-4Deductive Reasoning Lesson 2-5Postulates and Paragraph Proofs Lesson 2-6Algebraic Proof Lesson 2-7Proving Segment Relationships Lesson 2-8Proving Angle Relationships

7. Lesson 3 Contents Example 1Identify Hypothesis and Conclusion Example 2Write a Conditional in If-Then Form Example 3Truth Values of Conditionals OBJECTIVE: To analyze statements in if-then form (2.8.11Q) (M8.D.1.1) Key Concept: Conditional statements 1.If-then statement: hypothesis: If …, conclusion: then ….

8. Example 3-1a Identify the hypothesis and conclusion of the following statement. If a polygon has 6 sides, then it is a hexagon. Answer: Hypothesis: a polygon has 6 sides Conclusion: it is a hexagon hypothesis conclusion If a polygon has 6 sides, then it is a hexagon.

9. Example 3-1b Tamika will advance to the next level of play if she completes the maze in her computer game. Answer: Hypothesis: Tamika completes the maze in her computer game Conclusion: she will advance to the next level of play Identify the hypothesis and conclusion of the following statement.

10. Example 3-1c Identify the hypothesis and conclusion of each statement. a. If you are a baby, then you will cry. b. To find the distance between two points, you can use the Distance Formula. Answer: Hypothesis: you are a baby Conclusion: you will cry Answer: Hypothesis: you want to find the distance between two points Conclusion: you can use the Distance Formula

11. Example 3-2a Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. Answer: Hypothesis: a distance is determined Conclusion: it is positive If a distance is determined, then it is positive. Sometimes you must add information to a statement. Here you know that distance is measured or determined. Distance is positive.

12. Example 3-2b A five-sided polygon is a pentagon. Answer: Hypothesis: a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form.

13. Example 3-2c Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form. a. A polygon with 8 sides is an octagon. b. An angle that measures 45º is an acute angle. Answer: Hypothesis: a polygon has 8 sides Conclusion: it is an octagon If a polygon has 8 sides, then it is an octagon. Answer: Hypothesis: an angle measures 45º Conclusion: it is an acute angle If an angle measures 45º, then it is an acute angle.

14. Example 3-3a Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer: Since the result is not what was expected, the conditional statement is false. The hypothesis is true, but the conclusion is false. Yukon rests for 10 days, and he still has a hurt ankle.

15. Example 3-3b Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer: In this case, we cannot say that the statement is false. Thus, the statement is true. The hypothesis is false, and the conclusion is false. The statement does not say what happens if Yukon only rests for 3 days. His ankle could possibly still heal. Yukon rests for 3 days, and he still has a hurt ankle.

16. Example 3-3c Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer: Since what was stated is true, the conditional statement is true. The hypothesis is true since Yukon rested for 10 days, and the conclusion is true because he does not have a hurt ankle. Yukon rests for 10 days, and he does not have a hurt ankle anymore.

17. Example 3-3d Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer: In this case, we cannot say that the statement is false. Thus, the statement is true. The hypothesis is false, and the conclusion is true. The statement does not say what happens if Yukon only rests for 7 days. Yukon rests for 7 days, and he does not have a hurt ankle anymore.

18. Example 3-3e Determine the truth value of the following statements for each set of conditions. If it rains today, then Michael will not go skiing. a. It does not rain today; Michael does not go skiing. b. It rains today; Michael does not go skiing. c. It snows today; Michael does not go skiing. d. It rains today; Michael goes skiing. Answer: true Answer: false

19. REVIEW Write each statement in if-then form: 1.A 32-ounce pitcher holds a quart of liquid. 2. The sum of the measures of supplementary angles is 180. If a pitcher is a 32-ounce pitcher, then it holds a quart of liquid. If two angles are supplementary, then the sum of the measures of the angles is 180.

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