Geometry Theorems and Proofs Guide
Learn about proving the Midpoint Theorem and Angle Bisector Theorem using deductive reasoning and established postulates and theorems. Understand how to apply these concepts with step-by-step examples.
Geometry Theorems and Proofs Guide
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Presentation Transcript
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 • Postulates (These include properties from algebra) • Theorems that have already been proven
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
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
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
Practice work • P46 we 1-18all
