Chapter 6.2 Use Proportions to Solve Geometry Problems

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you set up a proportion to solve a geometry problem?

Back

To set up a proportion, identify two ratios that relate to the problem. Set them equal to each other and solve for the unknown.

Front

What is the scale factor in a scale drawing?

Back

The scale factor is the ratio of a length in the drawing to the corresponding length in the actual object. For example, a scale of 1:100 means 1 unit in the drawing represents 100 units in reality.

Front

If a model is 1 foot tall and the actual object is 20 feet tall, what is the scale factor?

Back

The scale factor is 1:20.

Front

How do you find the actual length of an object using a scale drawing?

Back

Multiply the length in the drawing by the scale factor. For example, if the drawing length is 5 cm and the scale is 1 cm = 2 m, the actual length is 5 cm * 2 m/cm = 10 m.

Front

What is the relationship between similar figures and proportions?

Back

Similar figures have the same shape but different sizes. The ratios of corresponding sides of similar figures are equal, which can be expressed as proportions.

Front

How do you solve for an unknown side in similar triangles?

Back

Set up a proportion using the lengths of the corresponding sides of the triangles. Cross-multiply and solve for the unknown.

Front

What is the formula for finding the area of a rectangle?

Back

The area of a rectangle is found using the formula: Area = length × width.

Front

If a rectangle has a length of 10 cm and a width of 5 cm, what is its area?

Back

The area is 10 cm × 5 cm = 50 cm².

Front

What is the formula for finding the perimeter of a rectangle?

Back

The perimeter of a rectangle is found using the formula: Perimeter = 2(length + width).