Postulates, Theorems, and Proofs

Goals:

· Properly use postulates and theorems· Know the kinds of reasons that can be

used in proofs

Postulate vs. Theorem

Reasons used in Proofs:

Midpoint Theorem

If M is the midpoint of

Draw a picture:

Now let's prove why it is true!

Given: M is the midpoint of

Prove:

Angle Bisector Theorem

If BX is the bisector of then

Draw a picture:

Now let's prove why it is true!!!

Given:

Prove:

Theorems

· If two lines intersect, then they intersect in exactly one point.

· Through a line and a point not on the line there is exactly one plane.

· If two lines intersect, then exactly one plane contains the lines.

Postulates

· Through any two points there is exactly one line.

· If two points are in a plane, then the line that contains the points is in that plane

· If two planes intersect, then their intersection is a line.

· Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.

· A line contains at least two points, a plane contains at least three points not all in one line; space contains at least four points not all in one plane.

P/T/P

Grade: 10Subject: Honors Geometry

Date: «date»

1

A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

2 AE + EF = AF

A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

3

A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

4

A Definition of MidpointB Defintion of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

5

A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

6

A Definiton of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

7

A Definition of Midpoint B Definition of Angle Bisector C Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

8

A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

9

A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector

Homework· Compare and contrast the Definition of Midpoint and the

Midpoint Theorem (1-2 paragraphs)·· Complete the following proof.