Proportions/scale factor

Front

What is a proportion?

Back

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

Front

Define scale factor.

Back

The scale factor is a number that scales, or multiplies, some quantity. In geometry, it is the ratio of the lengths of two corresponding sides of similar figures.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How do you find the scale factor between two similar figures?

Back

To find the scale factor, divide the length of a side of the larger figure by the length of the corresponding side of the smaller figure.

Front

If triangle A has sides of length 6, 8, and 10, and triangle B has sides of length 12, 16, and 20, what is the scale factor from triangle A to triangle B?

Back

The scale factor is 2.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the scale factor.

Front

If the scale factor of two similar triangles is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25.

Front

How can proportions be used to solve real-world problems?

Back

Proportions can be used to find unknown quantities in problems involving ratios, such as scaling recipes, maps, or models.

Front

If a car travels 300 miles on 10 gallons of gas, how many miles can it travel on 15 gallons of gas?

Back

450 miles.

Front

Solve for x: If triangle A has a side of length 4 and triangle B has a corresponding side of length 10, what is x if triangle A is similar to triangle B?

Back

x = 10.