Question

decide whether the red and blue polygons are similar.
the polygons are similar.
the polygons are not similar.

Explanation:

Step1: Identify polygon side lengths

The red polygon is a kite with 4 sides: two sides of length $\sqrt{3^2+3^2} = 3\sqrt{2}$, and two sides of length $\sqrt{3^2+3^2} = 3\sqrt{2}$ (it is a rhombus, specifically a square rotated 45 degrees).
The blue polygon is a kite with 4 sides: two sides of length 3, and two sides of length $\sqrt{3^2+3^2} = 3\sqrt{2}$.

Step2: Check side length ratios

For similarity, all corresponding side ratios must be equal. The ratio of red to blue sides would be $\frac{3\sqrt{2}}{3} = \sqrt{2}$ for one pair, and $\frac{3\sqrt{2}}{3\sqrt{2}} = 1$ for the other pair. These ratios are not equal.

Step3: Verify angle correspondence

All angles in the red polygon are 90° and 90° (since it's a square rotated). The blue polygon has two right angles and two angles that are not 90° (its non-right angles are 45° and 135°). Corresponding angles are not equal.

Answer:

The polygons are not similar.