Question

qadirilatral abcd diagonal ac and bd intersect each others such that ae/ec=be/ed then prove abcd is trapizum​

Answer 1

Join E to G on AD such that EG is Parallel to AB

Similarly join E to F on side BC such that EF is parallel to DC

Now in triangle ADC

AG/AD = AE/EC ( BY BPT)

Now in triangle ABC

AE/EC = CF/FB ( BY BPT)

so from the above two equation

AG/GD = BF/FC

So area of both the triangles are equal

Since are of both the triangles are equal and they both lie on the same base, so it is a trapezium