Answers to Homework 12)a) She assigns hours of homeworkb) No Conclusion c) He is not a math teacherd) No Conclusion 14)a) Stu loves Geometryb) No Conclusion.

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Presentation transcript:

Answers to Homework 12)a) She assigns hours of homeworkb) No Conclusion c) He is not a math teacherd) No Conclusion 14)a) Stu loves Geometryb) No Conclusion c) No Conclusiond) George is not my student 16)a) JL ┴ KMb) No Conclusion c) No Conclusiond) NOPQ is not a rhombus 18)a) No Conclusion b) Last is not a rhombus or a square c) PQRS is a rhombusd) No Conclusion

6-3 Indirect Proof

Indirect Proof 1. Assume temporarily that opposite of prove. 2. Then think how to contradict the info. 3. But this contradicts Given. 4. Therefore the temporary assumption that opposite of prove must be false. 5. It follows that Prove.

Ways to remember… Always (Assume) Take (Then) Bread (But) To (Therefore) Italy (In conclusion) The bread in Italy is not good.

Ways to remember what goes in the blanks… Olives (opp. Of prove) Taste (Think) Good (Given) On (Opp. Prove) Pizza (Prove)

Given: In parallelogram XYZW, m  X = 80° Prove: Parallelogram XYZW is not a rectangle. Assume temporarily that Parallelogram XYZW is a rectangle. Then rectangles have all right angles which means m  X = 90°. But this contradicts the given information that m  X = 80°. Therefore the temporary assumption that Parallelogram XYZW is a rectangle is false. It follows that Parallelogram XYZW is not a rectangle. EXAMPLE 1

Given: m  X ≠ m  Y Prove:  X and  Y are not both right angles Assume temporarily that  X and  Y are both right angles. Then m  X = 90° and m  Y = 90°. Using substitution, m  X = m  Y. But this contradicts the given information m  X ≠ m  Y. Therefore the temporary assumption that  X and  Y are both right angles is false. It follows that  X and  Y are not both right angles. TOO

Multiple Choice Theorem: A triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in <A and <B are both obtuse. Which theorem will Eduardo use to reach a contradiction? A) If two angles of a triangle are equal, the sides opposite those angles are equal. B) If two supplementary angles are equal, the angles each measure 90°. C) The largest angle in a triangle is opposite the longest side. D) The sum of the measures of the angles of a triangle is 180°. ANSWER: D

Starting with If, Then If they start with and If-Then— The “If” part is the GIVEN Then “Then” part is the PROVE

Try On Own (On WBs) Pg 215 #2-5 (only first sentence) Answers: 2. Assume temporarily that ∆ABC is not equilateral. 3. Assume temporarily that Doug is not Canadian. 4. Assume temporarily that a < b. 5. Assume temporarily that Kim is a violinist.

Homework Pg. 216 #1-10