1. Expectation: You will: 1. Write proofs in “If, then…” form. 2. Write the negations of “all,” “every” “no” and “there exists” statements. 3/7/2016 2-5: Verifying Segment Relationships 1

2. Jerry stated that squaring a number always results in a positive result. Is this statement true or false. If false, provide a counterexample. 3/7/2016 2-5: Verifying Segment Relationships 2

3. Equivalence Property of Congruence Theorem a. Congruence of segments is reflexive: b. Congruence of segments is symmetric: c. Congruence of segments is transitive: 3/7/2016 2-5: Verifying Segment Relationships 3

4. Parts of a Geometric Proof a. State the theorem (may already be done for you). b. State the given (hypothesis) and what you are trying to prove (conclusion). c. Draw a diagram. d. Start with the given and deduce statements until you reach the conclusion (connect the given and the prove with a logic chain). 3/7/2016 2-5: Verifying Segment Relationships 4

5. In order to be a good proof writer, you MUST know all of the postulates definitions and theorems. Take the next 15 minutes to make a complete list (not a part of your notes) of all of our postulates definitions and theorems up to this point. If you do not finish in the time allotted, it is expected that you will complete the list by class tomorrow. 3/7/2016 2-5: Verifying Segment Relationships 5

6. Prove the Symmetric Property of Congruence State the theorem: What is the given? What must we prove? 3/7/2016 2-5: Verifying Segment Relationships 6

7. Complete the Proof 3/7/2016 2-5: Verifying Segment Relationships 7

8. Let’s do another one together! Given: P, Q and S are collinear Prove: PQ = PS – QS 3/7/2016 2-5: Verifying Segment Relationships 8 PQ S

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10. Identify the “given” and the “prove.” The statement is not supposed to make sense. If a thingamabob is fluzzelled, then it has been whompied. 3/7/2016 2-5: Verifying Segment Relationships 10

11. Complete the proof below by filling in the blanks. 3/7/2016 2-5: Verifying Segment Relationships 11

12. Complete the Proof. 3/7/2016 2-5: Verifying Segment Relationships 12

13. Assignment 2-5-1 Skills Practice 2-7 3/7/2016 2-5: Verifying Segment Relationships 13

14. Write the negation of the following statement. The ball is blue. 3/7/2016 2-5: Verifying Segment Relationships 14

15. Write the negation of the given statement. Every ball is blue. 3/7/2016 2-5: Verifying Segment Relationships 15

16. Negating all, every and no statements. What would we need to show to prove the following statement is false? “Every car is black.” So how many non-black cars are needed for the negation? Write the negation of the given statement. 3/7/2016 2-5: Verifying Segment Relationships 16

17. Negating all, every and no statements. What would we need to show to prove the following statement is false? “All cheese is orange.” So how many non-orange cheeses are needed for the negation? Write the negation of the given statement. 3/7/2016 2-5: Verifying Segment Relationships 17

18. Negating all, every and no statements. What would we need to show to prove the following statement is false? “No triangles have right angles.” So how triangles with right angles are needed for the negation? Write the negation of the given statement. 3/7/2016 2-5: Verifying Segment Relationships 18

19. One more special type of negation. “There exists a plane that contains A, B, C and D.” How can we negate (make false) this statement? Write the negation of this statement. 3/7/2016 2-5: Verifying Segment Relationships 19

20. What is the negation of the statement, “No squares are triangles?” A. all squares are triangles B. all triangles are squares C. no triangles are squares D. there exists at least one square that is a triangle. E. There exists at least one triangle that is a square. 3/7/2016 2-5: Verifying Segment Relationships 20

21. Now back to proofs! 3/7/2016 2-5: Verifying Segment Relationships 21

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23. Assignment 2-5-2 pages 104-105, # 15-31 (odds), 39-45 (odds). 3/7/2016 2-5: Verifying Segment Relationships 23