Let ABCD be a rhombus. M, K, P, and E are the middle of the sides, respectively AB, BC, CD, AD.
Prove that MCRE is a rectangle.
The proof should begin by considering each of the triangles included in the ABCD rhombus: triangles ABC, BCD, ACD, ABD. In each of these triangles, the middle lines are drawn: MK, KR, PE, ME. By the property of the middle line in the triangle, MK is parallel to AC, KP is parallel to BD, EP is parallel to AC, ME is parallel to BD.
It follows that MK is parallel to EP, and KP is parallel to ME.
But AC and BD are diagonals of the rhombus ABCD, and they are perpendicular by property.
The ICRU means a rectangle.
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