Which of the following pairs of triangles are congruent by the SSS Congruence Theorem?(1 point)

Question

Responses

An illustration shows two similar triangles. Two sides and one angle of each triangle are marked as congruent.
Image with alt text: An illustration shows two similar triangles. Two sides and one angle of each triangle are marked as congruent.

An illustration shows two similar triangles. The corresponding sides of both the triangles are marked as congruent.
Image with alt text: An illustration shows two similar triangles. The corresponding sides of both the triangles are marked as congruent.

An illustration shows two similar triangles. One corresponding side and two angles of each triangle are marked as congruent.
Image with alt text: An illustration shows two similar triangles. One corresponding side and two angles of each triangle are marked as congruent.

An illustration shows two similar triangles. One side and two angles of each triangle are marked as congruent.

Answer 1

The SSS Congruence Theorem (Side-Side-Side) states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Let's analyze the options you provided:

1. Two sides and one angle of each triangle are marked as congruent.

   • This does not satisfy SSS, as it requires all three sides to be congruent.

2. The corresponding sides of both the triangles are marked as congruent.

   • This satisfies SSS, as all three sides are congruent.

3. One corresponding side and two angles of each triangle are marked as congruent.

   • This does not satisfy SSS; it suggests the use of the ASA (Angle-Side-Angle) theorem.

4. One side and two angles of each triangle are marked as congruent.

   • This also does not satisfy SSS; this is the AAS (Angle-Angle-Side) criterion.

Based on this analysis, the correct answer is the second option, where the corresponding sides of both triangles are marked as congruent, satisfying the SSS Congruence Theorem.