Question

question 9 (5 points)
under what circumstances are two nonright triangles congruent?
a) one side and one angle are equal
b) two angles are equal
c) three sides are equal
d) three angles are equal

Explanation:

For two triangles to be congruent, there are several congruence criteria.

• Option A: One side and one angle equal is not sufficient. For example, an angle - side combination may not fix the shape and size uniquely.
• Option B: Two angles equal only gives similarity (by AA similarity criterion), not congruence. Congruence requires information about sides to fix the size.
• Option C: By the SSS (Side - Side - Side) congruence criterion, if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
• Option D: Three angles equal gives similarity (by AAA similarity criterion), not congruence as the sides can be of different lengths.

Answer:

C. Three sides are equal