Question

Can you explian mid point theorem

Answer 1

Triangle Midpoint Theorem. Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

Answer 2

AM=BM [midpoint].
< AMP = <MBQ [Corresponding angles for parallel lines cut by an transversal].
<BQM=<QCP=<APM [Corresponding angles for parallel lines cut by an transversal].
<BMQ=<MAP [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]
AMP is congruent to MBQ. [ASA]
Therefore: AP=MQ=PC and MP=BQ=QC. 
Since midpoints are unique, and the lines connecting points are unique, the proposition is proven.