Identify the hypothesis and the conclusion: If two lines are parallel, then the lines are coplanar.

1. Conditional Statements LESSON 2-1 Additional Examples Identify the hypothesis and the conclusion: If two lines are parallel, then the lines are coplanar. In a conditional statement, the clause after if is the hypothesis and the clause afterthen is the conclusion. Hypothesis: Two lines are parallel. Conclusion: The lines are coplanar. Quick Check

2. Conditional Statements LESSON 2-1 Additional Examples Write the statement as a conditional: An acute angle measures less than 90º. The subject of the sentence is “An acute angle.” The hypothesis is “An angle is acute.” The first part of the conditional is “If an angle is acute.” The verb and object of the sentence are “measures less than 90°.” The conclusion is “It measures less than 90°.” The second part of the conditional is “then it measures less than 90°.” The conditional statement is “If an angle is acute, then it measures less than 90°.” Quick Check

3. Conditional Statements LESSON 2-1 Additional Examples Find a counterexample to show that this conditional is false: If x2 > 0, then x > 0. A counterexample is a case in which the hypothesis is true and the conclusion is false. This counterexample must be an example in which x2≥ 0 (hypothesis true) and x ≥ 0 or x < 0 (conclusion false). Because any negative number has a positive square, one possible counterexample is x = –1. Because (–1)2 = 1, which is greater than 0, the hypothesis is true. Because –1 < 0, the conclusion is false. The counterexample shows that the conditional is false. Quick Check

4. Conditional Statements LESSON 2-1 Additional Examples Use the Venn diagram below. What does it mean to be inside the large circle but outside the small circle? The large circle contains everyone who lives in California. The small circle contains everyone who lives in Anaheim. To be inside the large circle but outside the small circle means that you live in California but outside Anaheim. Quick Check

5. Conditional Converse Hypothesis Conclusion Hypothesis Conclusion x = 9 x + 3 = 12 x + 3 = 12 x = 9 Conditional Statements LESSON 2-1 Additional Examples Write the converse of the conditional: If x = 9, then x + 3 = 12. The converse of a conditional exchanges the hypothesis and the conclusion. So the converse is: If x + 3 = 12, then x = 9. Quick Check

6. = / The conditional is false. A counterexample is a = –5: (–5)2 = 25, and –5 5. Conditional Statements LESSON 2-1 Additional Examples Write the converse of the conditional, and determine the truth value of each: If a2 = 25, a = 5. Conditional: If a2 = 25, then a = 5. The converse exchanges the hypothesis and conclusion. Converse: If a = 5, then a2 = 25. Because 52 = 25, the converse is true. Quick Check

7. Conditional Statements LESSON 2-1 Additional Examples The Mad Hatter states: “You might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” Provide a counterexample to show that one of the Mad Hatter’s statements is false. The statement “I eat what I see” written as a conditional statement is “If I see it, then I eat it.” This conditional is false because there are many things you see that you do not eat. One possible counterexample is “I see a car on the road, but I do not eat the car.” Quick Check