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In quadrilateral ABCD P,Q,R and S …

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In quadrilateral ABCD P,Q,R and S are mid points prove the diagonal is trisected

    • Posted by Yoganshu Tripathi 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Shireen Gupta 6 years, 9 months ago

    Given ABCD is a parallelogram Hence AB || CD ⇒ AE || FC Also AB = CD (Opposite sides of parallelogram ABCD) ⇒ AE = FC (Since E and F are midpoints of AB and CD) In quadrilateral AECF, one pair of opposite sides are equal and parallel. ∴ AECF is a parallelogram. ⇒ AF || EC (Since opposite sides of a parallelogram are parallel) In ΔDPC, F is the midpoint of DC and FQ || CP Hence Q is the midpoint of DQ by converse of midpoint theorem. ⇒ DQ = PQ → (1) Similarly, in ΔAQB, E is the midpoint of AB and EP || AQ Hence P is the midpoint of DQ by converse of midpoint theorem. ⇒ BP = PQ → (2) From equations (1) and (2), we get BP = PQ = DQ Hence, the line segments AF and EC trisect the diagonal BD of parallelogram ABCD.

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