Solving Proportions & Pythagorean Theorem

Front

What is a proportion?

Back

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

Front

How do you solve a proportion?

Back

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

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Front

What is the formula to find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c².

Front

If a right triangle has legs of length 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 6² + 8² = c²; 36 + 64 = c²; c² = 100; c = 10.

Front

What does it mean if two ratios are in proportion?

Back

It means that the two ratios are equivalent, or that their cross products are equal.

Front

How can you check if two fractions are in proportion?

Back

Cross-multiply the fractions and see if the products are equal.

Front

What is the relationship between similar triangles and proportions?

Back

In similar triangles, the ratios of corresponding sides are equal, which means they can be expressed as proportions.

Front

What is the first step in solving for a variable in a proportion?

Back

Cross-multiply the two ratios.

Front

If x/4 = 3/12, what is the value of x?

Back

Cross-multiply: x * 12 = 4 * 3; x = 1.