1 / 9

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

orea
Download Presentation

Section 2-3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related