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Quadrilaterals — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsQuadrilaterals1 Mark
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Answer

  1. AC2 + BD2 = 4AB2
    Solution:
    ABCD is a rhombus. AB = BC = CD = DA
    In Rhombus, diagonals bisect each other at right angles.
    So, AO= CO and BO = DO
    In triangle AOB × AO2 + BO2 = AB2 (Pythagoras theorem)
    $\Big(\frac{1}{2}\text{AC}\Big)^2 + \Big(\frac{1}{2}\text{BD}\Big)^2 = \text{AB}^2$
    $\frac{\text{AC}^2}{4} + \frac{\text{BD}^2}{4} = \text{AB}^2$
    = AC2 + BD2 = 4AB2

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