InterviewSolution
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InterviewSolution
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Show that the line segments joining the mid points of the opposite sides of a quadrilateral and bisect each other. |
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Answer» Let ABCD be a quadrilateral. P, Q, R, S are the midpoints of sides of □ABCD. Join (P, Q), (Q, R), (R, S) and (S, P). In ΔABC; P, Q are the midpoints of AB and BC. ∴ PQ // AC and PQ = 1/2 AC ………….(1) Also from ΔADC S, R are the midpoints of AD and CD SR // AC and SR = 1/2 AC …………………(2) ∴ From (1) & (2) PQ = SR and PQ //SR ∴ □PQRS is a parallelogram. Now PR and QS are the diagonals of □ PQRS. ∴ PR and QS bisect each other. |
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