ΔABC and ΔDBC are on the same base BC and on opposite sides of BC. If O is the point of intersection of BC and AD, prove that:

Question

Philoid · Accepted Answer

Given: ΔABC and ΔDBC with common base BC.

To Prove:

Construction: Draw AM ⏊ BC and DN ⏊ BC

Proof:

In ΔAMO and ΔDNO

∠AOM = ∠DON [Vertically opposite angle]

∠AMO = ∠DNO [Both 90°]

ΔAMO ~ ΔDNO [By Angle-Angle sum criterion]

[Corresponding sides of similar triangles are in the same ratio] [1]

Now, we know that

Area of a triangle

Therefore,

[From [1]]

Hence, Proved