Question

Diagonals ac and bd intersect ai o. Area of aod is qual to area of boc prove that abcd is a trapezium

Answer 1

Answer:

Step-by-step explanation:

Given,

Diagonals AC and BD intersect at O. ar(ΔAOD) = ar(ΔBOC)

Proof:

A trapezium is a quadrilateral with one pair of opposite sides parallel.

Given

ar(ΔAOD) = ar(ΔBOC)

Add ar(ΔOAB) to both sides.

ar(ΔAOD) + ar(ΔOAB) =  ar(ΔBOC) + ar(ΔOAB)

=> ar(ΔADB) = ar(ΔCAB)

Now ΔADB and ΔCAB lie on same base AB, are equal in area and they lie between same parallel lines AB and DC

=> AB || DC (∵ Two triangles having same base and equal areas lie between same parallel lines.)

So, one of the opposite sides is parallel.

∴ ABCD is a trapezium.

Hence proved.