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 bisect each other. |
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Answer» Data : P, Q, R and S are mid-points of AB, BC, CD and DA respectively in quadrilateral ABCD. To Prove: PR and SQ line segments bisect mutually. Construction: Join the diagonal AC. Proof: In ∆ADC, S and R are the mid-points of AD and DC. ∴ SR || AC SR = \(\frac{1}{2}\)AC ………… (i) (Mid-point Theorem) Similarly, in ∆ABC, PQ || AC PQ = \(\frac{1}{2}\)AC …………. (ii) From (i) and (ii), SR = PQ and SR || PQ ∴ PQRS is a parallelogram. PR and SQ are the diagonals of parallelogram PQRS. ∴PR and SQ meet at O’. |
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