5-7: Similar Figures

Using proportions for dimensional analysis and problem solving

Vocabulary

Polygon

A closed figure made up of 3 or more line segments.

Similar Figures

Figures that have the same shape, but not necessarily the same size.

Corresponding sides

The sides of two or more polygons that are in the same relative position.

Corresponding angles

The angles of two or more polygons that are in the same relative position.

Examples

A) B)

10 ÷ 6 = 1.6666…

18 ÷ 10.8 = 1.6666…

21 ÷ 12.6 = 1.6666…

Steps in Solving

To determine if two figures are similar…

I.Determine if the corresponding angles are equal and/or the corresponding sides are proportional.

Steps in Solving

To determine if two figures are similar…

I.Determine if the corresponding angles are equal and/or the corresponding sides are proportional.

A) B)

Steps in Solving

To find the missing lengths of two similar polygons…

I.Write a proportion using the given corresponding lengths and missing length.

•Be sure to place the corresponding lengths, in the corresponding position in the proportion.

II.Use cross multiplication, or other strategies to solve the proportion.

Steps in Solving

To find the missing lengths of two similar polygons…

I.Write a proportion using the given corresponding lengths and missing length.

•Be sure to place the corresponding lengths, in the corresponding position in the proportion.

II.Use cross multiplication, or other strategies to solve the proportion.

C)

Steps in Solving

Scale Factor

The ratio formed by the corresponding sides of two or more similar figures.

Steps in Solving

Scale Factor

The ratio formed by the corresponding sides of two or more similar figures.

D) Find the Scale Factor of the two similar triangles.

Scale Factor:______________

Steps in Solving

Scale Factor

The ratio formed by the corresponding sides of two or more similar figures.

E)A picture 10 in tall and 14 in. wide is to be scaled to 1.5 in. tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar? Use the Scale Factor to solve.

Now try these…

1) A 5 ft person near a tree has a shadow of 12 ft long. The tree has a shadow of 42 ft long. What is the height of tree? (Drawing a rough sketch helps is solving).

2) The scale on a map is 1 inch = 20 miles. The distance from Fairfield to Hartford is 2.5 inches how many miles it from Fairfield to Hartford?

3) On a map 1 inch represents 25 miles. You measure the distance between two cities on a map and find the distance to be 5 ½ inches. Find the number of miles between the cities.