Using Proportions with Similar Figures Proportions, dilations, and scale drawings

Dilations create figures that have proportional sides 6 7.5 ---- = -------- 8 10

There are many uses of ratios and proportions There are many uses of ratios and proportions. We use them in map reading, making scale drawings and models, solving problems.

The most recognizable use of ratios and proportions is drawing models and plans for construction. Scale factors are used to approximate what the actual object will be like.

Two ratios that are equal Proportions Two ratios that are equal

A proportion is an equation that states that two ratios are equal, such as:

Similar Figures The Big and Small of it

Similar Polygons corresponding angles are congruent, and corresponding sides are proportional (in other words the sides must have lengths that form equivalent ratios)

Congruent figures have the same size and shape Congruent figures have the same size and shape. Similar figures have the same shape but not necessarily the same size. The two figures below are similar. You can write 2 kinds of proportions 2 Ways to write a proportion Corresponding Sides Big side 4 = 6 Sml side 2 3 Same – shape comparison Length 4 = 2 Width 6 3

Use a proportion to determine the missing side length.

Use a proportion to determine the height of the tree.

The two windows below are similar The two windows below are similar. Find the unknown width of the larger window.

These two buildings are similar. Find the height of the large building.