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Question
Draw a quadrilateral ABCD. Mark the mid-points E, F, G,H of the sides AB,BC,CD,DA respectively. Join EF,FG,GH and HE. Verify that the quadrilateral EFGH is a parallelogram.
Draw a quadrilateral ABCD. Mark the mid-points E, F, G,H of the sides AB,BC,CD,DA respectively. Join EF,FG,GH and HE. Verify that the quadrilateral EFGH is a parallelogram.
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Solution
Let ABCD be any quadrilateral. Join the midpoints of AB, BC, CD and DA represented by E, F, G and H.
Each diagonal, AC and BD, divides the quadrilateral into two triangles.
Since the mid-points of adjacent sides are joined EF, and GH will be parallel to diagonal AC and be equal to half of the diagonal.
Again FG and HE will be parallel to diagonal BD and be equal to half of the diagonal. So you have 2 pairs of opposite sides that are equal and parallel to each other, hence EFGH is a parallelogram.
Let ABCD be any quadrilateral. Join the midpoints of AB, BC, CD and DA represented by E, F, G and H.
Each diagonal, AC and BD, divides the quadrilateral into two triangles.
Since the mid-points of adjacent sides are joined EF, and GH will be parallel to diagonal AC and be equal to half of the diagonal.
Again FG and HE will be parallel to diagonal BD and be equal to half of the diagonal. So you have 2 pairs of opposite sides that are equal and parallel to each other, hence EFGH is a parallelogram.
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