Which statement is true about the congruence of triangles with corresponding sides equal?

Which statement is true about the congruence of triangles with corresponding sides equal?

• A. The corresponding sides are equal
• B. The triangles must be similar
• C. The corresponding angles are supplementary
• D. The perimeters are unequal

Answer: (A)

When two triangles are congruent, their corresponding parts match exactly in both size and shape. If all three pairs of corresponding sides are equal, that is enough to guarantee congruence (the SSS criterion). So stating that the corresponding sides are equal is a direct reflection of congruence and confirms that the triangles are the same in size and shape. As a consequence, corresponding angles must also be equal, and the perimeters must be the same. The idea that the triangles must be similar is true in the sense that congruent triangles are also similar, but similarity alone does not guarantee equal sides; equal corresponding sides give the stronger claim of congruence. The notion that corresponding angles would be supplementary is incorrect for congruent triangles, since their corresponding angles are equal. And saying the perimeters are unequal contradicts congruence, which requires equal perimeters.

When two triangles are congruent, their corresponding parts match exactly in both size and shape. If all three pairs of corresponding sides are equal, that is enough to guarantee congruence (the SSS criterion). So stating that the corresponding sides are equal is a direct reflection of congruence and confirms that the triangles are the same in size and shape.

As a consequence, corresponding angles must also be equal, and the perimeters must be the same. The idea that the triangles must be similar is true in the sense that congruent triangles are also similar, but similarity alone does not guarantee equal sides; equal corresponding sides give the stronger claim of congruence. The notion that corresponding angles would be supplementary is incorrect for congruent triangles, since their corresponding angles are equal. And saying the perimeters are unequal contradicts congruence, which requires equal perimeters.