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ABCD is a quadrilateral. E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram. |
Answer» Given that E, F, G and H are the midpoints of the sides of quad. ABCD. In ΔABC; E, F are the midpoints of the sides AB and BC. ∴ EF//AC and EF = 1/2 AC Also in ΔACD; HG // AC and HG = 1/2 AC ∴ EF // HG and EF = HG Now in □EFGH; EF = HG and EF // HG ∴ □EFGH is a parallelogram. |
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