Geometry Warm ups What is the relationship between the lengths of RS and ST? _ What is the relationship between the lengths of RT and ST? _ What is.

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Presentation transcript:

Geometry Warm ups What is the relationship between the lengths of RS and ST? ___ What is the relationship between the lengths of RT and ST? ___ What is the relationship between the measures of <A and <B? **Look at whiteboard What is the relationship between the measures of <B and <C? **Look at whiteboard 5) Write the sentence that helps you remember the special segments

5-4 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/Gross (Given) On (Opp. Prove) Pizza (Prove)

Example Answer: Assume temporarily that is a perpendicular bisector. State the assumption you would make to start an indirect proof for the statement is not a perpendicular bisector.

Example State the assumption you would make to start an indirect proof for the statement3x = 4y + 1. Answer: Assume temp. that 3x ≠ 4y + 1

TOO A. B. C. D.

TOO A. B. C. D.

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

5) Write a FULL Indirect Proof Given: 2r + 3 ≠ 17 Prove: r ≠ 7 Assume temporarily that r = 7. Then 2r + 3 = 2(7) + 3 = = 17. But this contradicts the given information 2r + 3 ≠ 17. Therefore the temporary assumption that r = 7 is false. It follows that r ≠ 7.

HW Pg. 359 #11-18, 27, 28 All

WBs—I’m calling on randoms, winners get a prize!!! Write ONLY the 1 st sentence in the proof 1. P: ∆ABC is equilateral. Answer: Assume temporarily that ∆ABC is not equilateral. 2. P: a > b Answer: Assume temporarily that a < b. 3. If a – b = 0, then a = b. Answer: Assume temp. than a not equal to b.