Question

b is the midpoint of $overline{ac}$. which statement best describes the relationship between triangles abd and cbd? triangles abd and cbd are congruent by the sss congruence postulate. triangles abd and cbd are similar by the sss similarity postulate. triangles abd and cbd are congruent by the sas congruence postulate.

Explanation:

Step1: Identify equal - side lengths

Since B is the mid - point of $\overline{AC}$, we have $AB = BC$. Also, $AD=CD = 15$ and $BD$ is common to both $\triangle ABD$ and $\triangle CBD$.

Step2: Apply congruence postulate

The SSS (Side - Side - Side) Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Here, $AB = BC$, $AD = CD$, and $BD=BD$. So, $\triangle ABD\cong\triangle CBD$ by the SSS Congruence Postulate.

Answer:

Triangles ABD and CBD are congruent by the SSS Congruence Postulate.