1. **State the problem:** Given that AC is the angle bisector of \(\angle BAD\), prove that \(\triangle ABC \cong \triangle ADC\). 2. **Identify given information:** - AC bisects \(\angle BAD\), so \(\angle BAC = \angle DAC\). - Segments AB and AD are marked equal. - AC is common to both triangles. 3. **Write the statements and reasons:** **Statement 1:** \(AB = AD\) **Reason 1:** Given (marked with tick marks on AB and AD) **Statement 2:** \(\angle BAC = \angle DAC\) **Reason 2:** AC is the angle bisector of \(\angle BAD\) **Statement 3:** \(AC = AC\) **Reason 3:** Reflexive property (common side) **Statement 4:** \(\triangle ABC \cong \triangle ADC\) **Reason 4:** ASA (Angle-Side-Angle) congruence criterion 4. **Explanation:** - Since AC bisects \(\angle BAD\), the two angles at A in triangles ABC and ADC are equal. - AB and AD are equal by given. - AC is common to both triangles. - Therefore, by ASA, the two triangles are congruent. This completes the proof.