1. Bellwork Find m  1 and m  2 if m  1 = 8x + 18 and m  2 = 16x – 6 and m  1 and m  2 are supplementary. A.m  1 = 106, m  2 = 74 B.m  1 = 74, m  2 = 106 C.m  1 = 56, m  2 = 124 D.m  1 = 14, m  2 = 166

2. A.A B.B C.C D.D A.24 B.42 C.68 D.84 Bellwork The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle?

3. Unit 3 Lesson 3 Conditional Statements Honors Geometry

4. Objectives I can recognize and write conditional statements I can use logic to make valid conclusions

5. Definition Conditional Statement – A statement generally written in the form If “p”, then “q” where: p: hypothesis - the information or event that must occur FIRST q : conclusion – the information or event that will occur second, as a result of the hypothesis

6. Identify the Hypothesis and Conclusion 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 HINT: A figure or object must exist first before a label / name can be applied to it!

7. Identify the Hypothesis and Conclusion 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.

8. 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 Which of the choices correctly identifies the hypothesis and conclusion of the given statement? To find the distance between two points, you can use the Distance Formula.

9. Write in “If – Then” Form 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.

10. A.A B.B C.C D.D 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°. Which of the following is the correct if-then form of the given statement? An angle that measures 45° is an acute angle.

11. Related Conditionals There are four statements that can be made from the same given information – Conditional – Converse – Inverse – Contrapositive The Conditional and the Contrapositive are Logically Equivalent (they should mean the same thing) The Converse and the Inverse are Logically Equivalent

12. Conditional If p, then q. Ex: If your grade is a 93, then you have earned an “A.”

13. Converse In order to form the converse of a conditional statement you reverse the order In general we write: If q, then p. Ex: If you have earned an “A,” then your grade is a 93. Conditional: If p, then q Does this mean the same as the conditional?

14. Inverse In order to form the inverse of a conditional statement, you negate everything In general we write: If not p, then not q. Ex: If your grade is not a 93, then you have not earned an “A.” Does this mean the same as the conditional? Conditional: If p, then q

15. Contrapositive To form the contrapositive of a conditional statement, you reverse and negate everything. In general we write: If not q, then not p. Ex: If you did not earn an “A,” then your grade was not a 93. Conditional: If p, then q Does this mean the same as the conditional?

16. 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. 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.

17. 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. 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.

18. A.A B.B C.C D.D 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?