Question

If AD=BC,Prove that AC=BD

Answer 1

△DEC,△AEB△DEC,△AEB are both isosceles. 

Remark: It is useful to note that AB∥DCAB∥DC, so ABCDABCD is an isosceles trapezoid, and it is a useful lemma that the diagonals of any isosceles trapezoid are equal.

Also, AD=BC⟺AB∥DC AD=BC⟺AB∥DC is a useful lemma.