Question

AB and CD are parallel sides of trapezium ABCD. Diagonals AC and BD intersect at O. prove that ar(ΔAOD) = ar(ΔBOC).​

Answer 1

Explanation:

Given:→ ABCD is a trapezium with AB || DC and Diagonal AC and BD intersect each other at O. Proof: → In ∆ADC and ∆BDC, ΔADC and ΔBDC are on the same base DC and between same parallel AB and DC.

Answer 2

Answer:

Look, I have calculated it, considering ABCD as an Isosceles trapezium.

Explanation:

If you can prove ∆AOD & ∆BOC congruent, then you can easily prove that their areas are equal because in two congruent triangles all sides, and angles and dimensions are equal. So, you can prove that They occupy equal areas.

I have used the S.A.S rule of congruency here. You can also try the S.S.S rule of congruency to prove it, as it is an *Isosceles Trapezium*.

Thank you... Hope it works for you.☺️☺️