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Piyush365

Asked: October 5, 2026In: Class 9 Maths

Is the Midpoint Theorem for Quadrilaterals (Theorem 9) true when the quadrilateral is non-convex? How about when it is self-intersecting? Experiment and check. The pictures may look strange, but the theorem appears to be true. (i) Can you explain why this is so? See the geometric reasoning in the text. (ii) There is one exception: In a very special case the Varignon parallelogram becomes a single segment. When will this happen? (iii) Does your reasoning apply even when ABCD is non-planar?

Yes, it holds in both cases. (i) The Midpoint Theorem on triangles formed by diagonals still ensures opposite sides are parallel and equal to half the diagonal. (ii) It degenerates into a segment when diagonal AC is parallel to BD ...