Question

angle bisector:
ad is the angle bisector of $angle bac$
$angle bad \cong \angle cad$
dc bisects $angle acb$
which parts of the triangles are congruent?
a) $angle a \cong \angle b$
b) $angle 1 \cong \angle 2$
c) $angle 3 \cong \angle 4$
a $square$ b $square$ c $square$

Explanation:

Step1: Recall angle bisector definition

An angle bisector splits an angle into two congruent angles.

Step2: Match to given diagram

DC bisects $\angle ACB$, so it splits $\angle ACB$ into $\angle 1$ and $\angle 2$.

Answer:

B) $\angle 1 \cong \angle 2$