Hello, Ragnarok!

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

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.'