Proving Theorems

Proving Theorems

THEOREMA result that has been proved to be true (using facts that were already known).MIDPOINT THEOREM

What is MIDPOINT??MidpointIs the middle point of a line segment. It is equidistant from both end points, and it is the centroid, both of the segment and of the endpoints.

Midpoint theoremIf M is the midpoint of AB, then AM = AB and MB is ABProve: AM = AB ; MB= ABA M B M is the midpoint of AB.GivenAM = MB or AM = MB~Definition of MidpointAM + MB = ABSegment addition postulate

AM + AM = AB or 2AM = ABSubstitution property (steps 2 and 3)

AM = ABDivision Property

MB = ABSubstitution Property

Angle Bisector TheoremWhat Is Angle Bisector??

Angle BisectorA line that splits an angle into two equal angles. ("Bisect" means to divide into two equal parts.)

Angle Bisector Theorem

Given: If AD bisects