To determine if any of the given triangles are congruent by the SSS (Side-Side-Side) Congruence Theorem, we must compare the lengths of the sides of the triangles.
- Triangle #1 has sides measuring 2.5 cm, 6.75 cm, and 8 cm.
- Triangle #2 has two sides measuring 2.5 cm and 8 cm, but we do not know the length of the third side as it is defined by the angle (60°) between them. Therefore, we cannot match it to Triangle #1.
- Triangle #3 has sides measuring 2.5 cm, 6.75 cm, and 8 cm, but it is given in a different configuration (with an angle), so it does not directly provide the necessary information based on the third side.
Now checking for potential congruence:
- Triangle #1 has side lengths: 2.5 cm, 6.75 cm, 8 cm.
- Triangle #3 has sides that include a side of length 8 cm alongside sides of 2.5 cm and 6.75 cm as well.
Since Triangle #3 also has the sides 2.5 cm, 6.75 cm, and 8 cm, we can say:
Triangle #1 and Triangle #3 are congruent by the SSS Congruence Theorem.
Thus, the answer is:
Triangle 1 and Triangle 3 are congruent.
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