Similar Figures

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What does it mean for two figures to be proportional?

Back

Two figures are proportional if the ratios of their corresponding sides are equal.

Front

How do you find the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the length of the corresponding side of the other figure.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what are the lengths of the sides of a similar triangle with a scale factor of 2?

Back

The lengths of the sides of the similar triangle would be 6 cm, 8 cm, and 10 cm.

Front

What is the relationship between the heights and shadows of similar figures?

Back

In similar figures, the ratio of the heights is equal to the ratio of the lengths of their shadows.

Front

If a 5 ft tall person casts a 2 ft shadow, how tall is a 10 ft tall person’s shadow?

Back

The 10 ft tall person would cast a shadow of 4 ft.

Front

What is a scale in the context of maps?

Back

A scale is a ratio that compares a distance on the map to the actual distance it represents in real life.

Front

If a map has a scale of 1 inch:50 miles, how many miles does 3 inches represent?

Back

3 inches represents 150 miles.

Front

How do you set up a proportion to solve for an unknown height using similar figures?

Back

Set up a proportion using the known heights and shadows, such as (height1/shadow1) = (height2/shadow2).

Front

What is the formula to find the actual distance using a map scale?

Back

Actual distance = distance on map × scale factor.