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Section 2-3

Section 2-3. Proving theorems Midpoint theorem Angle bisector theorem. Define: deductive reasoning. Deductive reasoning- proving statements by reasoning from accepted postulates definitions theorems, and the given information. Reasons Used in Proofs. Given information Definitions

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Section 2-3

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  1. Section 2-3 • Proving theorems • Midpoint theorem • Angle bisector theorem

  2. Define: deductive reasoning • Deductive reasoning- proving statements by reasoning from accepted postulates definitions theorems, and the given information

  3. Reasons Used in Proofs • Given information • Definitions • Postulates (These include properties from algebra) • Theorems that have already been proven

  4. If M is the midpoint of AB, A M B Midpoint Theorem then AM = 1/2 AB and MB = 1/2AB. Prove it!! Given M is the midpoint of AB If M is the midpoint of AB then AM = MB def of the midpoint If M is between A and B then AM + MB = AB segment add postulate If AM = MB and AM + MB = AB then AM + AM = AB substitution If two terms are like terms then 2AM = AB combining like terms If 2AM = AB then AM = ½ AB division property If AM = MB and AM = ½ AB then MB = ½ AB substitution

  5. If BX is the bisector of <ABC, • then m<ABX = ½ m<ABC and m<XBC = ½<ABC Angle Bisector Theorem A X B C

  6. If Y is the midpoint of ZX, then ZY=YX • If m 1 =m 2, then WY is the angle bisector of ZWX • m 3 + m 4 = 180 • If ZY = ½ ZX, then Y is the midpoint of ZX • ZY + YX = ZX • If WY bisects ZWX, then m 2 = ½ m ZWX W 1 2 3 4 Z Y X Name the definition, postulate, or theorem that justifies the statement about the diagram

  7. Practice work • P46 we 1-18all

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