Question

ABCD is quadrilateral in which diagonal AC and BD intersect each other at a E.show that area of TRIANGLE AED x AREA OF TRIANGLE BEC = AREA OF TRIANGLE ABE x AREA OF TRIANGLE CDE

Answer 1

ABCD is a quadrilateral in which diagonals AC and BD of a quadrilateral ABCD intersect each other at E.
To prove: ar (AEB) × ar (CED) = ar (AED) × ar (BEC)
Construction: Draw AM ⊥ BD and CN ⊥ BD.

Proof:
LHS = ar (AEB) × ar (CED)

= ar (BPC) × ar (APD)
= ar (AED) × ar (BEC)
= RHS [Hence proved]

Answer 2

Ans. See the attached pic for solution