Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–2) Then/Now New Vocabulary Key Concept: Conditional Statement Example 1: Identify the Hypothesis.

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Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 2–2) Then/Now New Vocabulary Key Concept: Conditional Statement Example 1: Identify the Hypothesis and Conclusion Example 2: Write a Conditional in If-Then Form Example 3: Truth Values of Conditionals Key Concept: Related Conditionals Key Concept: Logically Equivalent Statements Example 4: Related Conditionals

Then/Now Analyze statements in if-then form. Write converses, inverses, and contrapositives.

Vocabulary conditional statement if-then statement hypothesis conclusion related conditionals converse inverse contrapositive

Points, Lines and Planes Postulate or Axiom Statement that is accepted as true without proof.

Concept

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

Example 1 Identify the Hypothesis and Conclusion B. Identify the hypothesis and conclusion of the following statement. 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.

A.A B.B C.C D.D Example 1 A.Hypothesis: You will cry. Conclusion: You are a baby. B.Hypothesis: You are a baby. Conclusion: You will cry. C.Hypothesis: Babies cry. Conclusion: You are a baby. D.none of the above A. Which of the choices correctly identifies the hypothesis and conclusion of the given conditional? If you are a baby, then you will cry.

A.A B.B C.C D.D Example 1 A.Hypothesis: You want to find the distance between 2 points. Conclusion: You can use the distance formula. B.Hypothesis: You are taking geometry. Conclusion: You learned the distance formula. C.Hypothesis: You used the distance formula. Conclusion: You found the distance between 2 points. D.none of the above B. Which of the choices correctly identifies the hypothesis and conclusion of the given conditional? To find the distance between two points, you can use the Distance Formula.

Example 2 Write a Conditional in If-Then Form A. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. Measured distance is positive. Answer:Hypothesis: A distance is measured. Conclusion: It is positive. If a distance is measured, then it is positive.

Example 2 Write a Conditional in If-Then Form B. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. 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.

A.A B.B C.C D.D Example 2 A.If an octagon has 8 sides, then it is a polygon. B.If a polygon has 8 sides, then it is an octagon. C.If a polygon is an octagon, then it has 8 sides. D.none of the above A. Which of the following is the correct if-then form of the given statement? A polygon with 8 sides is an octagon.

A.A B.B C.C D.D Example 2 A.If an angle is acute, then it measures less than 90°. B.If an angle is not obtuse, then it is acute. C.If an angle measures 45°, then it is an acute angle. D.If an angle is acute, then it measures 45°. B. Which of the following is the correct if-then form of the given statement? An angle that measures 45° is an acute angle.

Concept

Example 4 Related Conditionals NATURE Write the converse, inverse, and contrapositive of the following true statement. Determine the truth value of each statement. If a statement is false, give a counterexample. Bats are animals that can fly. Bats are not birds, they are mammals. Bats have modified hands and arms that serve as wings. They are the only mammals that can fly.

Example 4 Related Conditionals Conditional:First, rewrite the conditional in if-then form. If an animal is a bat, then it can fly. This statement is true. Converse:If an animal can fly, then it is a bat. Counterexample: A bird is an animal that can fly, but it is not a bat. The converse is false.

Example 4 Related Conditionals Inverse:If an animal is not a bat, then it cannot fly. Counterexample: A bird is not a bat, but it is an animal that can fly. The inverse is false. Contrapositive:If an animal cannot fly, then it is not a bat. The converse is true.

Example 4 Related Conditionals CheckCheck to see that logically equivalent statements have the same truth value. Both the conditional and contrapositive are true.  Both the converse and inverse are false. 

A.A B.B C.C D.D Example 4 A.All 4 statements are true. B.Only the conditional and contrapositive are true. C.Only the converse and inverse are true. D.All 4 statements are false. Write the converse, inverse, and contrapositive of the statement The sum of the measures of two complementary angles is 90. Which of the following correctly describes the truth values of the four statements?

End of the Lesson