Question

In the adjoining figure, DE || BC.
Prove that
(i) ar(∆ACD) = ar(∆ABE)
(ii) ar(∆OCE) = ar(∆OBD).​

Answer 1

Given

1. Area of ∆BDE =Area of ∆CDE ( Any Two Triangles Standing on Same base between the same parallel lines have equal area )

2. ∆ADE +∆BDE= ∆ADE + ∆ CDE (Fact 1.)

   Area of ∆ABE = Area of ∆ ADC (Whole part Axiom)

3. Area of ∆ABE - Area of pam ADOE = Area of ∆ACD - Area of pam ADOE

   (Being common in both Triangles)

    Area of OBD = Area of OCE