Ratios and Proportions

Standard

G.SRT.5 Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Goals for this section:

Students will be able to create ratios and proportions. Ratios compare two quantities.

What is a ratio?

A ratio compares two or more quantities. It can be written in three ways:

We generally write ratios in the same units and in simplified form.

Examples:

Create a ratio of the following:

length of a tennis racket: 2 ft 4 in and length of a table tennis paddle 10 in.
the width of a 46 in tree to its 8 ft height.

Answers:

How to use a ratio

Sometimes a ratio can be used to find measurements/quantities. This usually involves knowing the total quantity.

Examples:

1. The measures of two complimentary angles are in the ratio 1:5. What are the measures of the angles?

We know that complimentary angles add up to 90. One of the angles is 1 part of 90 while the other is 5 parts of 90. So we can create an equation x + 5x = 90. Notice the coefficients come from the ratio. Now solve for x, but remember, the question asks for what the measurements of the angles are.

Answer:

2. The lengths of the sides of a triangle have a ratio of 3:4:5. The perimeter is 96 cm. What are the lengths of each side?

The perimeter of a triangle is simply adding up all the sides. Our equation will be 3x + 4x + 5x = 96. Solve for x, but remember, the question asks for what the measurements of the angles are.

Answer:

What is a proportion?

A proportion is when two or more ratios are equivalent. We generally use proportions when we know two objects are similar.

When setting up a proportion, make sure to be consistent! See example below.

Cross Multiply Method

Proportions can be used to find unknown measurements of similar objects.

Cross multiplying means to create a "cross" or an "x" to indicate which numbers will be multiplied with each other. These numbers that are multiplied together are then set equal to each other. This is demonstrated to the left.