MathDB

In a quadrilateral, the two segments connecting the midpoints of its opposite sides are equal in length. Prove that the diagonals of the quadrilateral are perpendicular.
(In other words, let

M,N,P,

and

Q

be the midpoints of sides

AB,BC,CD,

and

DA

in quadrilateral

ABCD

. It is known that segments

MP

and

NQ

are equal in length. Prove that

AC

and

BD

are perpendicular.)

Problem Statement