University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2021
Views:

115

Pages:

5
Author:

Adelyn Pacheco

Today's objectives: 1. Use the midpoint and angle bisector theorems to justify geometric statements. 2. Use previously learned postulates, theorems, and definitions to justify algebraic and geometric statements. 3. Continue to work on partially completed proofs. Geometry/Trigonometry II 2.3 Proving Theorems Name Theorem 2-1: The Midpoint Theorem 1 If M is the midpoint of AB, then AM = AB and MB = AB. A M B *Def: If M is the midpt of As, then AM=MB If then Given: M is the midpoint of overline AB Prove: AM = 1/2 * AB and MB = 1/2 * AB A M B Proof: Statements Reasons 1. M is the midpoint of overline AB 1. Given 2. AM MB or AMMB 2. def. of midpoint AM MB AB 3. Seg. Addition Post. 4. AMAMAB 2AM AB 4. substitution property 5. AM = 1/2 * AB 5. Division Prop. 6. MB = 1 2 A dot B 6. Substitution : Example: Given: M is the midpoint of overline AB , N is the midpoint of overline CD . and AB = CD What can you deduce from this information? Draw an accurate picture of the two segments and their midpoints and write out at least one new factual statement about the picture. Theorem 2-2: The Angle Bisector Theorem If overline BX is the bisector of < ABC , then m < ABX = 1/2 * m < ABCan * dm < XBC = 1/2 * m < ABC bisede Given: BX bisects CABC PIOVE MLABX MLABC = m angle X*beta*L = 1 2 m angle A beta C (6) Proof: Statements Reasons 1. overline BX is the bisector of < ABC 1. Given 2. angle ABX cong< XBC 2. Definition of < Bisector 3. m angle ABX +m angle XBC=m angle ABC 3. Angle Addition Post. 4. m angle ABX +m angle ABX=m angle ABC 4. Substitution 5. m angle ABX = 1 2 m angle ABC 2MLABXMLAROC 5. Division Prop. 6. m < XBC = 1/2 * m < ABC 6. Substitution Reasons used in proofs: 11. Given information 13. Postulates 2. Definitions 4. Theorems