Question

in the given figure,abcd is a parallelogram

Answer 1

1- IN triangle FEC and AEB -
angle FCE = angle BEA (V. O. A)
angle BAE = angle EFC (alternate angles)
lly angle EAB =angle ECF (alternate angles)
so triangle FEC ~ triangle AEB.(AAA rule )...........(1)
2- In triangle FEC and triangle FAD
angle F =angle F ( common)
angle CEF =angle DAE (corresponding angles)
lly Angle ADC =angle ECF (C. A ")
so triangle FEC ~ triangle FAD (AAA rule).......... (2)
3- in triangle AEB and triangle FAD
from (1) and (2)- these are also congruent!!!

I think this is the only way to do these.