Questions: If triangle ABC is congruent to triangle DBC, then line BC bisects the angle ACD. A. True B. False

Solution Steps

The problem states that triangles \( \triangle ABC \) and \( \triangle DBC \) are congruent.

Since \( \triangle ABC \cong \triangle DBC \), all corresponding sides and angles of these triangles are equal. This means:

• \( AB = DB \)
• \( AC = DC \)
• \( \angle BAC = \angle BDC \)
• \( \angle ABC = \angle DBC \)
• \( \angle ACB = \angle DCB \)

Given that \( \triangle ABC \cong \triangle DBC \), the line segment \( BC \) is common to both triangles. Since \( \angle BAC = \angle BDC \), the line segment \( BC \) bisects the angle \( \angle ACD \).

Final Answer