statements
1. draw $\overline{ad}$, the angle bisector of $\angle cab$.
2. $\angle cad \cong \angle bad$
3. $\overline{ab} \cong \overline{ac}$
4. $\overline{da} \cong \overline{da}$
5. dashed box
6. $\angle b \cong \angle c$
reasons
1. construction of angle bisector
2. dashed box
3. given
4. reflexive property of congruence
5. sas congruence theorem
6. corresponding parts of congruent triangles are congruent.
options: transitive property of congruence, definition of angle bisector, $\overline{db} \cong \overline{dc}$, $\triangle adb \cong \triangle adc$

Question

Accepted Answer

### For Reason 2:
# Brief Explanations:
To determine the reason for $ \angle CAD \cong \angle BAD $, we recall that an angle bisector divides an angle into two congruent angles. Since $ \overline{AD} $ is the angle bisector of $ \angle CAB $, by the definition of an angle bisector, $ \angle CAD $ and $ \angle BAD $ must be congruent.
# Answer:
Definition of angle bisector

### For Statement 5:
# Brief Explanations:
We know from the given information and previous steps: $ \overline{AB} \cong \overline{AC} $ (given), $ \angle CAD \cong \angle BAD $ (from angle bisector definition), and $ \overline{DA} \cong \overline{DA} $ (reflexive property). Using the SAS (Side - Angle - Side) Congruence Theorem, we can conclude that $ \triangle ADB \cong \triangle ADC $ because we have two sides and the included angle of one triangle congruent to the corresponding two sides and included angle of the other triangle.
# Answer:
$ \triangle ADB \cong \triangle ADC $

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Question

Explanation:

For Reason 2:

Answer:

For Statement 5: