Question

determine if the two triangles are congruent. if they are, state the postulate or theorem that proves they are congruent.

Explanation:

Step1: Identify Equal Sides

In triangles \( \triangle ABC \) and \( \triangle DBC \):

• \( AB = DB \) (two tick marks),
• \( AC = DC \) (three tick marks),
• \( BC = BC \) (common side, reflexive property).

Step2: Apply Congruence Postulate

By the Side - Side - Side (SSS) Congruence Postulate, if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. Here, \( AB = DB \), \( AC = DC \), and \( BC = BC \), so \( \triangle ABC \cong \triangle DBC \) by SSS.

Answer:

The two triangles (\( \triangle ABC \) and \( \triangle DBC \)) are congruent by the SSS (Side - Side - Side) Congruence Postulate.