Question

Are the following figure always, sometimes, or never similar?

Explain.

1. two triangles.
2. two squares.
3. two rectangles

Answer 1

Step 1: Check the similarity of two triangles.

Two triangles are similar only when all the corresponding angles are equal and all the corresponding side lengths are proportional.

Step 2: Check the similarity of two squares.

Two squares are always similar because in square all angles are fixed of $90°$ and all sides are equal.

Step 3: Check the similarity of two rectangles.

Two rectangles are sometimes similar only when all the corresponding angles are equal and the lengths of the corresponding sides are proportional.