Forum

Diagonals AC and BD...
 
Notifications
Clear all

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(△AOD) = ar(△BOC). Prove that ABCD is a trapezium.

  

0
Topic starter

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(△AOD) = ar(△BOC). Prove that ABCD is a trapezium.

1 Answer
0

Given,

ar(△AOD) = ar(△BOC)

To Prove

ABCD is a trapezium.

Proof:

ar(△AOD) = ar(△BOC)

⇒ ar(△AOD) + ar(△AOB) = ar(△BOC) + ar(△AOB)

⇒ ar(△ADB) = ar(△ACB)

Areas of △ADB and △ACB are equal.

∴ they must lying between the same parallel lines.

∴ AB ∥  CD

∴ ABCD is a trapezium.

Share:

How Can We Help?