Question

question 10 of 10
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 recall the definition of congruent triangles. Congruent triangles are triangles that have the exact same shape and size, which means their corresponding angle measures and side lengths are equal.

• Option A: Having the same angle measures means the triangles are similar (same shape but not necessarily same size), not congruent.
• Option B: Just "size" is too vague; congruence requires both angle and side - length correspondence.
• Option C: Vertices are points, and congruence is about angles and side lengths, not vertices in the sense of just having the same vertices (which doesn't define congruence).
• Option D: This matches the definition of congruent triangles as they need to have the same angle measures (for shape) and side lengths (for size).

Answer:

D. angle measures and side lengths