You can't be sure there is a right angle. Why do you have to prove it?
If the original isosceles trapezoid has AC⊥BD condition, it can be proved that △BDE is an isosceles right triangle.
Otherwise, the angle cannot be proved to be correct.
Connect alternating current
∫AD‖CE,AD=CE
A quadrilateral is a parallelogram.
∴AC=DE
∵ABCD is an isosceles trapezoid.
∴AC=BD
∴BD=DE
Find that △BDE is an isosceles triangle.