ABCD is a quadrilateral in which diagonals AC and BD intersect at a point E. Show that
ar(AED) ar(BEC) = ar(ABE) ar(CDA) .

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Solution

ABCD is a quadrilateral in which diagonals AC and BD of a quadrilateral.
ABCD intersect each other at E
To prove: $a r (A E B) \times a r (C E D) = a r (A E D) \times a r (B E C)$
Construction: Draw AM $⊥$ BD and CN $⊥$ BD
Proof:
L.H.S= $= a r (A E B) \times a r (C E D) = a r (B P C) \times a r (A P D) = a r (A E D) \times a r (B E C) = R . H . S p r o v e d$

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In quadrilateral ABCD, diagonals AC and BD intersect at point E. Such that AE : EC = BE : ED. Then, ABCD is a parallelogram.

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