Lesson 1: Scaled Copies

Property

If one figure is a scaled copy of another, two key properties are always true:

1. All corresponding angles are congruent (have the same measure).
2. The ratio of any pair of corresponding side lengths is constant and equal to the scale factor.

Examples

Property

The scale factor is the ratio of the lengths in the new figure to the corresponding lengths in the original figure.

Examples

• A map has a scale factor of $\frac{1}{10000}$. A road that is 3 cm long on the map is $3 \times 10000 = 30000$ cm, or 300 meters, in real life.
• A triangle with a base of 8 inches is enlarged to a similar triangle with a base of 20 inches. The scale factor is $\frac{20}{8} = 2.5$.
• To reduce a 12-foot wall to fit on a blueprint with a scale factor of $\frac{1}{48}$, its length on the blueprint is $12 \times \frac{1}{48} = \frac{1}{4}$ foot, or 3 inches.

Explanation

The scale factor is the number you multiply by to change the size of a figure. A scale factor greater than 1 makes the figure bigger (an enlargement), while a factor between 0 and 1 makes it smaller (a reduction).

Property

To find the length of a side in a scaled copy, multiply the length of the corresponding side in the original figure by the scale factor ($k$).