Question

perpendicular bisector of a trapezium​

Answer 1

Answer:

Let AD∩BC={E} and EN be a median of ΔDEC.

Thus, since ∡EDC=∡ECD, we obtain that ED=EC and from here EN is an altitude of ΔDEC.

Also, since ∡EAB=∡EBA, we obtain that EA=EB and since EN⊥AB,

we see that EN is a perpendicular bisector of AB and we are done!