Question

the following is the proof of the base angles theorem. fill in the blank with the correct statement.
proof:

1. given isosceles △abc with $overline{ab}congoverline{bc}$, i can construct $overleftrightarrow{bd}$, the angle bisector of ∠b.

2.

1. i also know that line segments are congruent to themselves, so $overline{bd}congoverline{bd}$ by the reflexive property of congruence.
2. i now have two pairs of sides and an included angle that are congruent, so i know that △abd≅△cbd by the sas congruence theorem.
3. finally, corresponding parts of congruent triangles are congruent by the cpctc theorem, so ∠a≅∠c.

(1 point)

Explanation:

Step1: Recall angle - bisector property

Since $\overrightarrow{BD}$ is the angle - bisector of $\angle B$, we have $\angle ABD\cong\angle CBD$.

Answer:

$\angle ABD\cong\angle CBD$