16-3 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 corresponding sides are proportional.

Front

What is the scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of two corresponding sides of similar figures. It indicates how much one figure has been enlarged or reduced compared to the other.

Front

How do you find the height of an object using shadows?

Back

You can use the property of similar triangles. If two objects cast shadows, the ratio of their heights is equal to the ratio of the lengths of their shadows.

Front

If a 10 m tall pole casts an 8 m shadow, what is the height of a building that casts a 14 m shadow?

Back

Using the ratio: (Height of pole / Length of pole's shadow) = (Height of building / Length of building's shadow). The height of the building is 17.5 m.

Front

What is the formula for finding the height of an object using similar triangles?

Back

Height of object = (Height of known object / Length of known object's shadow) * Length of object's shadow.

Front

If two similar triangles have sides in the ratio 2:3, what is the scale factor?

Back

The scale factor is 2/3.

Front

How do you determine the distance on a map using a scale?

Back

To find the distance on a map, use the scale ratio. For example, if the scale is 3 cm:18 km, then for every 3 cm on the map, it represents 18 km in reality.

Front

If Oakdale and Woodridge are 54 km apart, how far apart are they on a map with a scale of 3 cm:18 km?

Back

Using the scale, the distance on the map is 9 cm.

Front

What is the relationship between corresponding angles in similar figures?

Back

Corresponding angles in similar figures are equal.

Front

If a statue is 42.9 ft tall and casts a 253.1 ft shadow, how long is the shadow of a 6.2 ft tall man?

Back

Using the ratio of heights to shadows, the man's shadow is 36.6 ft.