Question

1. describe how to use ratios to determine whether two shapes are similar.

Explanation:

To determine if two shapes are similar using ratios, first check if their corresponding angles are equal. Then, calculate the ratios of their corresponding side lengths. If all the ratios of corresponding side lengths are equal (this is called having a constant scale factor), and the corresponding angles are congruent, the two shapes are similar. For example, for two triangles, if \(\angle A=\angle D\), \(\angle B = \angle E\), \(\angle C=\angle F\) (angle - angle - angle similarity condition in part) and \(\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=k\) (where \(k\) is a constant, the scale factor), the triangles are similar.

Answer:

Check if corresponding angles are equal and if the ratios of all corresponding side lengths are the same. If both conditions are met, the two shapes are similar.