Question

1. draw two polygons that are similar but could be mistaken for not being similar. explain why they are similar.

Explanation:

Step1: Draw similar polygons

Draw a square with side - length 2 units and another square with side - length 4 units. They are similar because all their corresponding angles are equal (each angle is 90 degrees) and the ratios of their corresponding side - lengths are equal. The ratio of the side - lengths of the second square to the first square is $\frac{4}{2}=2$.

Step2: Explain similarity

Two polygons are similar if their corresponding angles are congruent and the ratios of their corresponding side - lengths are equal. In the case of the two squares, the angle - congruence condition is met as all interior angles of a square are 90 degrees, and the side - length ratio is consistent for all sides.

Step3: Draw non - obvious similar polygons

Draw a rectangle with length 4 units and width 2 units, and another rectangle with length 8 units and width 4 units. At first glance, they might not seem similar due to their different sizes, but they are. The corresponding angles are all 90 degrees, and the ratio of the lengths ($\frac{8}{4} = 2$) and the ratio of the widths ($\frac{4}{2}=2$) are equal.

Answer:

You can draw a square of side - length 2 and a square of side - length 4 for similar polygons. And a rectangle of length 4 and width 2 and a rectangle of length 8 and width 4 for polygons that could be mistaken for not being similar but are actually similar. The reason for similarity is that corresponding angles are equal and ratios of corresponding side - lengths are equal for similar polygons.