Question

Given that ∠ABC ≅ ∠DBE, which statement must be true?

∠ABC ≅ ∠ABD

∠ABD ≅ ∠CBE

∠CBD ≅ ∠DBE

∠CBD ≅ ∠ABC​

Answer 1

∠ABD ≅ ∠CBE

Explanation:

So we know that ∠ABC ≅ ∠DBE. Those angles equal the same thing. Let's represent that with x.

So does ABD = CBE?

Well we can model that with our xs.

ABD = ABC + CBD

so ABD = x + CBD

CBE = DBE + CBD

so CBE = x + CBD

Look at what we have!

x + CBD = x + CBD.

You can tell that ∠ABD ≅ ∠CBE because those given angles are equal to each other.

Or for an easier (but lazier) method, you can just look at the diagram, which is actually drawn to a reasonable scale. You can tell right off the bat that none of the other options work.