Question

Given: BC bisects DBE. Prove: ABD is congruent to ABE

Answer 1

The proof that ∠ABD is congruent to ∠ABE would be detailed below to your understanding

What are Congruent Angles and Bisectors?

Congruent angles are angles that are equal and identical to each other when measured.

A Bisector is a line that divides another line or angle into two equal parts.

Given that;

Line BC divided angle DBE into two equal parts.

It is seen that line BC extends to point A while dividing the external angle DBE into two equal parts.

Therefore, ∠ABD is congruent to ∠ABE.

Answer 2

See below

Explanation:

BC bisects <DBE and if AC is a straight line then you have that:

<ABD + <DBC = 180 (straight angle because of line AC)

<ABE + <CBE = 180 ( straight angle because of line AC)

Because BC bisects <DBE => < DBC = <CBE

So <ABD and <ABE must be the same to both sum 180 when added < DBC