1. Learning Goals Recognize and analyze a conditional statement. Write postulates about points, lines, and planes as conditional statements ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

2. Conditional Statement A type of statement that can be written in if-then form The part after the “if” called the hypothesis the part after the “then” is called the conclusion To do well in Geometry, you must study. If you want to do well in Geometry, then you must study. Rewrite the conditional statement in if-then form.

3. If you want to do well in Geometry, then you must study. hypothesis: conclusion: You want to do well in Geometry. You must study. Identify the hypothesis and conclusion.

4. All mammals breathe oxygen. conditional statement: If an animal is a mammal, then it breathes oxygen. hypothesis: conclusion: An animal is a mammal It breathes oxygen

5. A blue sky means no rain today. conditional statement: If the sky is blue, then it will not rain today hypothesis: conclusion: The sky is blue. It will not rain today.

6. Converse A conditional statement with the hypothesis and conclusion reversed. If you want to do well in Geometry, then you must study. If you study, then you will do well in Geometry.

7. Write the converse, If an animal is a fish, then it can swim. If an animal can swim, then it is a fish. true or false?FALSE

8. Write the converse If the sky is blue, then it will not rain today. If it does not rain today, then the sky is blue.

9. Write the converse true or false?FALSE

10. A conditional statement, or conjecture, is true only when every possible case of the statement is true. To show a statement is false only one example showing the statement doesn’t work is needed. The example is called a counterexample. In a counterexample the hypothesis is true, but the conclusion is false. every time something involving a statement happens

11. Write the converse true or false?FALSE counterexample:

12. Show the following conjecture is false by finding a counterexample. The difference of two positive numbers is always positive. If-then form: Counterexample: If two positive numbers are subtracted, then the answer will be positive.

13. Show the following conjecture is false by finding a counterexample. Any number raised to the 3 rd power is greater than the original number. If-then form: Counterexample: If a number is raised to the 3 rd power, then the answer will be greater than the original number.

14. Through any two points, there exists exactly one line. A B If two points exist, then exactly one line can be drawn through the points.

15. A line A B If a line exists, then at least two points are on the line. contains at least two points This Postulate is the ___ of the last postulate. a)conditional b)converse

16. If two lines intersect, then their intersection is exactly one point. P

17. Through any three noncollinear points there exists exactly one plane. P R Q

18. A plane contains at least three noncollinear points. a)conditional b)converse P R Q This Postulate is the ___ of the last postulate.

19. If two points lie in a plane, then the line containing them is also on the plane. P Q

20. If two planes intersect, then their intersection is a line.

21. p. 8: 34 – 39 p. 75 : 2, 9, 11, 14, 15, 18, 35 – 38