Given: Line BD, Line AE, <B is congruent to <D Prove: AB over ED is equal to BC over DC

Question

They are vertical triangles.

B E

C

A D

This is the best way I can depict the drawing

Answer 1

I am going to make some assumptions here.

You have the lines BD and AE which intersect at C.

By ∠D i assume you mean ∠ADB and ∠B is ∠EBD.

∠BCE = ∠ACD because they are vertical angles.

Therefore the third angles in the 2 triangles are equal.

And that means the 2 triangles are similar.

By similar logic you can prove triangle BCA similar to triangle ECD

Then you have your conclusion because corresponding sides of similar triangles are in proportion.