Similar Triangles

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

The ratio of the lengths of corresponding sides of two similar triangles.

Use the proportion of corresponding sides. If triangle A is similar to triangle B, then A's side length divided by B's side length equals the scale factor.

All corresponding angles are equal.

The lengths of corresponding sides are proportional.

Convert the map distance to actual distance using the scale ratio.

Set up a proportion: (height of statue)/(length of statue's shadow) = (height of man)/(length of man's shadow). Solve for the length of the man's shadow.

Height = (length of shadow) * (height of object being compared) / (length of shadow of object being compared).

Use the scale to set up a proportion: 3 cm/18 km = x cm/54 km. Solve for x to find the distance on the map.

The length of the shadow can be used to find the height of an object using the properties of similar triangles.