Ratios and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as 'a:b' or 'a/b'.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, expressed as 'a/b = c/d'.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and then solve for the unknown variable.

Front

What is the sum of the angles in a triangle?

Back

The sum of the angles in a triangle is always 180 degrees.

Front

If the angles of a triangle are in the ratio 2:4:9, how do you find the measures of the angles?

Back

Let the angles be 2x, 4x, and 9x. Set up the equation 2x + 4x + 9x = 180, then solve for x.

Front

What is an extended ratio?

Back

An extended ratio compares three or more quantities, such as a:b:c.

Front

If a triangle's angles are in the ratio 1:2:3, what are the measures of the angles?

Back

The angles are 30°, 60°, and 90°.

Front

How do you express a ratio in simplest form?

Back

To express a ratio in simplest form, divide both terms by their greatest common divisor.

Front

What is the relationship between similar triangles and ratios?

Back

In similar triangles, corresponding sides are in proportion, meaning their ratios are equal.

Front

If two ratios are equivalent, what can be said about their cross products?

Back

If two ratios are equivalent, the cross products are equal (a/b = c/d implies a*d = b*c).