Question

traingle ABC and DBC have common base BC Prove that Area of triangle ABC /area of triangle DBC =AO /BC​

Answer 1

The given figure can be re-drawn as shown in the above figure where AE and DF are heights of Δ ABC and Δ BCD respectively.

Now ΔAOE and ΔFOD are similar.

As ∠EOA=∠FOD [Opposite angle], ∠AEO=∠DFO [right-angles] and ∠EAO=∠FDO [AE∥FD and AD intersector].

So AE/DF = AO/OD _______(1)

now,

ar( ABC)/ar( DBC)=

1/2 * BC*AE / 1/2 * BC/ FD

= AE/FD = AO /OD

(using (1) )

hope its help u