Post on 15-Apr-2018
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
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A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector
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A Definition of MidpointB Defintion of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector
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A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector
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A Definiton of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector
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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
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A Definition of MidpointB Definition of Angle BisectorC Angle Addition PostulateD Segment Addition PostulateE Midpoint TheoremF Angle Bisector TheoremG Definition of Segment Bisector
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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.