Line segment DB is an angle bisector of ∠ADC. Which statement best describes the relationship between the triangle ABD and CBD? a.) Triangles ABD and CBD are congruent by the SSS Congruence Postulate.
b.) Triangles ABD and CBD are similar by the SSS Similarity Postulate.
c.) Triangles ABD and CBD are congruent by the SAS Congruence Postulate.
d.) Triangles ABD and CBD are similar by the SAS Similarity Postulate.

c.) Triangles ABD and CBD are congruent by the SAS Congruence Postulate.

Step-by-step explanation:

Line segment DB divides <ADC into two congruent angles. That is:

<ADB is congruent to <CDB

Segment DB of ∆ABD is congruent to segment DB of ∆CBD.

Also, Segment AD of ∆ABD is congruent to segment CD of ∆CBD.

This means two sides (DB and AD) and an included angle (<ADB) of ∆ABD are congruent to the corresponding two sides (DB and CD) and included angle (<CDB) of ∆CBD.

Therefore, by the SAS Congruence Postulate, ∆ABD is congruent to ∆CBD.