Similar Figures and Proportions

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 their corresponding sides are in proportion.

Front

What does it mean for angles in similar figures?

Back

All angles in similar figures are congruent (equal).

Front

What is the relationship between the sides of similar figures?

Back

The corresponding sides of similar figures are in proportion.

Front

If two triangles are similar, what can we say about their corresponding sides?

Back

The ratios of their corresponding sides are equal.

Front

How do you find the height of an object using similar figures?

Back

You can set up a proportion using the heights and corresponding lengths of similar figures to solve for the unknown height.

Front

If a tree's shadow is 12 ft and a 3 ft tall pole's shadow is 1 ft, how tall is the tree?

Back

Using proportions: (Height of tree / 12 ft) = (3 ft / 1 ft) → Height of tree = 36 ft.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

If two similar figures have a scale factor of 3:2, what does this mean?

Back

It means that for every 3 units in one figure, there are 2 units in the other figure.

Front

What is the scale factor?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar figures.

Front

If the length of one side of a triangle is 6 cm and the corresponding side of a similar triangle is 9 cm, what is the scale factor?

Back

The scale factor is 9/6 or 3/2.