1. It’s already Tuesday! 1. You need your journal. Unit 1 test is on Friday What did the one wall say to the other wall? I’ll meet you at the corner

3. Let’s add some vocabulary

5. Point - an exact location in space with an indefinite shape and size Line - an object with no thickness that continues infinitely in two directions

6. Line segment - an object consisting of two endpoints and all of the points between them Plane - a flat surface that continues infinitely in all directions

7. Ray – an object with one endpoint that continues infinitely in one direction Collinear - points that lie on the same line Coplanar - points that lie on the same plane

8. What is the intersection of AE and AD? What is the intersection plane ADC and CG? What is the intersection of plane AED and plane EHG?

9. Given: 4(x – 1) = 7x – 10 Given: 8x + 15 = 4x - 9 Prove: x = 2 Prove: x = -6 Prove using a 2-column proof

10. You only need your journal today Don’t forget to turn in your homework (the 2 problems from yesterday) What do you call a cow with no legs? Ground Beef!

11. Conditional Statement A logical statement that has 2 parts; a hypothesis and a conclusion. It is written in the form of “if-then” h c

12. Hypothesis –the “if” part of a conditional statement Conclusion – the “then” part of a conditional statement If today is Tuesday, then tomorrow is Wednesday.

13. More Examples If it is raining, then there are clouds in the sky. If x + 7 = 10, then x = 3

14. Why do we learn conditionals statements? Conditional statements are the form for which theorems are written in geometry

15. There are 3 related conditionals The negation is always the opposite meaning of the original statement.

16. Converse Exchange the hypothesis and the conclusion. c h Converse – If tomorrow is Wednesday, then today is Tuesday Original statement – if today is Tuesday, then tomorrow is Wednesday.

17. Inverse Negate both the hypothesis and conclusion. h’ c’ Original statement – if today is Tuesday, then tomorrow is Wednesday. Inverse – if today is not Tuesday, then tomorrow is not Wednesday

18. Contrapositive Exchange the hypothesis and conclusion of the inverse. c’ h’ Original statement – if today is Tuesday, then tomorrow is Wednesday. Contrapositive – If tomorrow is not Wednesday, then today is not Tuesday.

19. Cloe will go to the movies if she finishes her homework. If Cloe finishes has homework, then she can go to the movies. If an animal is a bird, then it has wings Change each to a conditional statement All birds have wings

20. Counterexample Not all conjectures are true. In order to prove a conjecture false you use a counterexample. All you need to is 1 counterexample to prove a conjecture false.

21. If an angle measures 90°, then it is a right angle. Biconditional -When a conditional and its converse are both true. (then use if and only if) An angle is a right angle if and only if it measures 90° Converse – If an angle is a right angle, then it measures 90°

23. Example Write the converse, inverse, and contrapositive of the conditional. Decide if each statement is true or false. If a dog is a Great Dane, then it is large.