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A NSWERS TO E VENS 2) Given, Mult., Divis. 4) Given, Add., Sub., Divis. 6) Given, Mult., Distr., Sub., Add., Divis. 8) FL = AT, Reflex, Add, Seg Add, FA = LT 10) Given, Angle Add, Subst, Reflex, Subtr

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2-3 P ROVING T HEOREMS

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M IDPOINT Definition: If M is the midpoint of AB, then AM = MB or AM MB Midpoint Theorem: If M is the midpoint of AB, then AM = ½AB and MB = ½AB. A M B

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Angle Bisector The definition and Theorem is just like the Midpoint ones!! Copy from the overhead.

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C OUPLE OF Q UESTIONS : What makes something a theorem? Some one proved it How can you tell apart the midpoint/angle bisector definitions and theorems? Definition uses = to Theorem uses = ½ What are the reasons that you are allowed to use in a proof? Given Definition Postulate Property Theorems that have already been proved

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E XAMPLE If OZ bisects XOY, find m ZOB. A 180 B 0 O X 110 Y 40 Z 70 35 75

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TOO Page 45 #1-9 (use the picture!) Answers: 1) Angle Addition Postulate 2) Segment Addition Postulate 3) Angle Addition Postulate 4) Definition of a Midpoint 5) Midpoint Theorem 6) Definition of Segment Bisector 7) Definition of Segment Bisector 8) Angle Bisector Theorem 9) Definition of Angle Bisector

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H OMEWORK Page 46 #1-18, skip #12 Flash cards Def. of Midpoint Midpoint Theorem Def. of Angle Bisector Angle Bisector Theorem

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ANSWERS TO WORKSHEET 1) 14 2) 24 3) 53 4) 50 5) 6 7) 20 8) 25 9) 43 10) Both pairs opp. Sides cong. 11) 1 pair is cong. and parallel 12) Both opp sides.

ANSWERS TO WORKSHEET 1) 14 2) 24 3) 53 4) 50 5) 6 7) 20 8) 25 9) 43 10) Both pairs opp. Sides cong. 11) 1 pair is cong. and parallel 12) Both opp sides.

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