Question

Prove the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures.

Answer 1

http://openstudy.com/updates/536d77ede4b0b55c8e78452e
That should help. Jim had a thorough explanation.

Answer 2

Angles 2 and 3 equal by vertical angle property
Angles 1 and 4 equal by property of alternate interior angles

Two triangles are congruent by AAS.
Therefore all corresponding sides of triangles are equal, cutting diagonals in half.