Which of the following pairs of triangles are congruent by the SSS Congruence Theorem?(1 point)
Responses
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.
Image with alt text: An illustration shows two similar triangles. One side and two angles of each triangle are marked as congruent.
An illustration shows two similar triangles. Two sides and one angle of each triangle are marked as congruent.
The pair of triangles that are congruent by the SSS Congruence Theorem is the one where two sides and one angle of each triangle are marked as congruent.
The pair of triangles that are congruent by the SSS Congruence Theorem is the one shown in the last option: "An illustration shows two similar triangles. Two sides and one angle of each triangle are marked as congruent."
To determine which pairs of triangles are congruent by the SSS Congruence Theorem, we need to look for triangles that have matching side lengths.
The SSS Congruence Theorem states that if the corresponding sides of two triangles are congruent, then the triangles are congruent. It means that if all three sides of one triangle are congruent to all three sides of another triangle, then the two triangles are congruent.
Looking at the given options:
1. The first option shows two triangles with corresponding sides marked as congruent. This satisfies the SSS Congruence Theorem.
2. The second option shows one corresponding side and two angles marked as congruent. This is not enough information to determine congruence using the SSS Congruence Theorem.
3. The third option shows one side and two angles marked as congruent. Again, this is not enough information to apply the SSS Congruence Theorem.
4. The fourth option shows two sides and one angle marked as congruent. This satisfies the SSS Congruence Theorem.
Based on the information provided, the pairs of triangles that are congruent by the SSS Congruence Theorem are the first and the fourth options.