Question

6. In triangle ABC, a line XY is drawn parallel to side BC. B is extended to E in such a
way that BE is parallel to AC and C is extended to F in such a way that CF is parallel
to AB. A line from E is drawn to F through X and Y. Prove that ar (AABE) - ar (AACF).​

Answer 1

Answer:

ar (∆ABE)=ar(∆ACF)

Step-by-step explanation:

in BXFC , XF||BC,CF||XB hence it is a parallelogram , now in BEYC ,BC||EY,BE||YC hence it is a parallelogram , parallelogram BXFC=BEYC having same base BC and same parallel XY||BC , now ar ∆ AEB =1÷2 (BEYC) ,ar ∆ ACF=1÷ 2 (BXFC) , hence ar AEB=ar ACF