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.