Question

1. An equilateral triangle is similar to a scalene triangle.

2. Two congruent polygons are similar.

3. Two rectangles are similar.

Can you please tell me if each of these are always, sometimes, or never true.

Answer 1

1. Similarity in triangles refers to equal angles. An equilateral triangle will always have all three angles being at 60 degrees, whereas a scalene triangle will have different values for all angles.

So the answer is - never true

2. In order for two polygons to be similar, they must be proportional. In order for two polygons to be congruent, they must be proportional and of the same size, or exactly the same. Thus, similarity is a component of congruency, and two congruent polygons will always be similar.

So, always true.

3. If two rectangles are proportional, they are similar. If not , they are not similar. With two random rectangles, either could be the case.

So, it is sometimes true.