1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates
14 - Reflection/Rotation

 

 Proving Theorems

 

Objective:

    • To be able to prove a theorem

Lesson 2-2 Proving Theorems:

    Theorems: statements that are proved. The Midpoint Theorem is a theorem. It states that 'If M is the midpoint of AB then AM = ½AB and MB = ½AB'. When a person is told to prove a theorem they are usually given the 'Given' and what to 'Prove'. 

Theorem 2-1 If M is the midpoint of AB then AM = ½AB and MB = ½AB Theorem 2-2 If BX is the bisector of <ABC, then m<ABX = ½m<ABC and m<XBC = ½m<ABC For example, Given: M is the midpoint of Segment AB Prove: AM = ½AB; MB = ½AB Statement 1. M is the midpoints of segment AB 2. Segment AM Segment MB, or AM = MB 3. AM + MB = AB 4. AM + AM = AB, or 2AM = AB 5. AM = ½AB  6. MB = ½AB Reasons 1. Given 2. Definition of midpoint 3.Segment Addition Postulate 4.Subsitiution Property (Steps 2 and 3) 5.Division Prop. of  = 6.Subsititution Property. (Steps 2 and 5)

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