Hi grizzlyjoker -

(a) Prove that the diagonals divide the rhombus into 4 identical (congruent) triangles. Then use the fact that two equal angles that add up to 180 degrees (where the diagonals meet) must each be 90 degrees.

(b) In addition to joining the four median points of the sides of the quadrilateral, join the two diagonals as well. Then use similar triangles to prove that the opposite sides of the inner quadrilateral are parallel in pairs to the two diagonals.

(c) Use the fact that the gradient of the line joining is ; repeat for the other two points, and then say that the gradients are equal.

Can you do them now?

Grandad