Question

use the image to answer the question. image long description consider the following proof. what theorem is being proved? given: isosceles △abc with (overline{ab}congoverline{bc}) prove: (angle acongangle c) theorem table statements reasons 1. isosceles △abc with (overline{ab}congoverline{bc}) 1. given 2. (overrightarrow{bd}) the angle - bisector of (angle b) 2. construction 3. (angle abdcongangle cbd) 3. definition of angle bisector 4. (bdcong bd) 4. reflexive property of congruence 5. (\triangle abdcong\triangle cbd) 5. sas congruence theorem 6. (angle acongangle c) 6. cpctc theorem

Explanation:

Step1: Analyze the given and prove statements

We are given an isosceles triangle $\triangle ABC$ with $AB\cong BC$ and we need to prove $\angle A\cong\angle C$.

Step2: Review the proof steps

The proof constructs the angle - bisector of $\angle B$, uses the definition of angle - bisector, reflexive property, SAS (Side - Angle - Side) congruence theorem and CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem.

Step3: Identify the theorem

The theorem being proved is that the base angles of an isosceles triangle are congruent.

Answer:

The base - angles of an isosceles triangle are congruent.