Provide an appropriate response.In triangle A, the longest side is twice as long as the shortest side. In triangle B, the longest side is also twice as long as the shortest side. If this is the only information you have about the two triangles, can you conclude that they must be similar? If you think that the two triangles must be similar, explain your answer. If you do not think that the triangles must be similar, sketch a counterexample.

Question

What will be an ideal response?

Answer 1

Answers will vary. The triangles do not have to be similar. Students should sketch two triangles which are not similar. In each triangle, the longest side should be twice the shortest side.