Question

which best completes the following sentence? triangles are congruent if they have the same ______. a. angle measures b. size c. vertices and angles d. angle measures and side lengths

Explanation:

To determine the correct answer, we analyze the definition of congruent triangles. Congruent triangles are defined as triangles that have the exact same shape and size. This means their corresponding sides are equal in length (same side lengths) and their corresponding angles are equal in measure (same angle measures).

• Option A: Having the same angle measures only means the triangles are similar (same shape, not necessarily same size), so A is incorrect.
• Option B: "Size" is a vague term. Just same size without considering angles or side lengths precisely isn't the definition, so B is incorrect.
• Option C: Vertices are points, and congruence is about sides and angles, not just vertices and angles. So C is incorrect.
• Option D: This matches the definition of congruent triangles (same angle measures and side lengths), so D is correct.

Answer:

D. angle measures and side lengths