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 or when all four vertices are collinear. (iii) Yes, it applies even for non-planar quadrilaterals.
Class 9 maths ganita manjari part 2 chapter 12 question answer
Class 9 Ganita Manjari Part 2 chapter 12 Quadrilaterals solutions
Yes, Varignon’s theorem holds generally. (i) The proof relies entirely on applying the triangle Midpoint Theorem to triangles formed by diagonals AC and BD; midpoints always form pairs of opposite sides parallel to and half the length of each diagonal. (ii) The Varignon parallelogram flattens into a single straight line segment when the two diagonals AC and BD are parallel lines (in self-intersecting figures) or when the four vertices are collinear. (iii) Yes, because each set of three vertices defines a flat triangle where the Midpoint Theorem remains valid in 3D space.
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