Prove that the line segments joining the midpoints of the opposite sides of a quadrilateral bisect each other.
We have quadrilateral with midpointsCode:A P B o * o * o * * S * * Q o o * * * * o * * * * o * * * * o D R C
Draw diagonals and
Theorem: The line segment joining the midpoints of two sides of a triangle
. . . . . . . .is parallel to and one-half the length of the third side.
Theorem: If two sides of a quadrilateral are parallel and equal,
. . . . . . . .the quadrilateral is a parallelogram.'