Question

question 7 of 10
if two triangles are congruent, which of the following statements must be
true? check all that apply.

a. the corresponding angles of the triangles are congruent.

b. the triangles have the same shape, but not the same size.

c. the triangles have the same shape and size.

d. the corresponding sides of the triangles are congruent.

Explanation:

To determine the correct statements about congruent triangles, we recall the definition of congruent triangles: two triangles are congruent if their corresponding sides and corresponding angles are equal, meaning they have the same shape and size (as opposed to similar triangles, which only have the same shape but not necessarily the same size).

• Option A: Since congruent triangles have equal corresponding angles, this statement is true.
• Option B: This describes similar triangles, not congruent ones. Congruent triangles have the same size, so this statement is false.
• Option C: By definition, congruent triangles have the same shape (due to equal angles) and the same size (due to equal sides), so this statement is true.
• Option D: Congruent triangles have equal corresponding sides, so this statement is true.

Answer:

A. The corresponding angles of the triangles are congruent.
C. The triangles have the same shape and size.
D. The corresponding sides of the triangles are congruent.