If two sides of a triangle are proportional to the corresponding sides of another triangle, then the

triangles are similar.

Is this Always True, Sometimes True, or Never True?

If you have to construct the second triangle, do you not see the two proportional sides flapping at an arbitrary angle?

It is always true if the included angles are equal. As it is, it is sometimes true.

This statement is called the Side-Side-Side (SSS) similarity theorem and it is Always True. If two triangles have their corresponding sides in proportion, then they are similar triangles.

To determine whether the statement "If two sides of a triangle are proportional to the corresponding sides of another triangle, then the triangles are similar" is always true, sometimes true, or never true, we need to consider the conditions under which triangles are similar.

Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. This condition is known as the Side-Angle-Side (SAS) similarity criterion.

In the given statement, it is mentioned that two sides of a triangle are proportional to the corresponding sides of another triangle. This condition satisfies one part of the SAS criterion. However, it does not mention anything about the corresponding angles.

Therefore, based on the given statement, we cannot conclusively determine whether the triangles are similar. The statement is sometimes true because, in addition to the sides being proportional, we need to ensure that the corresponding angles are congruent to establish similarity.