Question

Which statement is true?

The triangles are not similar, but they are congruent.
The triangles are neither similar nor congruent.
The triangles are similar by the SAS similarity theorem.
The triangles are similar by the SSS similarity theorem.

Answer 1

I don’t have the diagram or any side/angle measures, so I can’t pick one choice for you. A couple quick points that help immediately:

- The first choice ("not similar, but congruent") is impossible: congruent triangles are always similar (they have the same shape and size), so that option is false.
- To decide between the remaining options, use these tests:
- SSS similarity: all three pairs of corresponding side lengths are proportional (a1/a2 = b1/b2 = c1/c2).
- SAS similarity: two pairs of corresponding side lengths are proportional and the included angles between those sides are equal.
- Neither: if neither of the above similarity tests holds, the triangles are not similar (and thus not congruent).

If you post the diagram or give the corresponding side lengths and/or angle measures, I’ll check the ratios/angles and tell you which statement is correct with a short justification.