Question

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

Explanation:

Step1: Recall similarity criteria

Two polygons are similar if their corresponding angles are equal and the ratios of their corresponding side - lengths are equal.

Step2: Draw and explain polygons

For example, draw two rectangles of different sizes. Let one rectangle have side - lengths 2 and 4, and the other have side - lengths 4 and 8.

• The corresponding angles of both rectangles are all 90 degrees.
• The ratio of the shorter sides is $\frac{2}{4}=\frac{1}{2}$, and the ratio of the longer sides is $\frac{4}{8}=\frac{1}{2}$. So, they are similar. But at first glance, if one doesn't measure the sides or consider the angle - equality carefully, they might think they are just two different rectangles and not similar.

Answer:

Draw a rectangle with side - lengths 2 and 4 and another rectangle with side - lengths 4 and 8. They are similar because corresponding angles are equal (all 90 degrees) and the ratios of corresponding side - lengths are equal ($\frac{2}{4}=\frac{4}{8}=\frac{1}{2}$), but might be mistaken for not being similar without careful inspection.