Pythagorean Theorem

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). It can be expressed as: a² + b² = c².

Front

What is a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers (a, b, c) that satisfy the Pythagorean theorem, meaning a² + b² = c². An example is (3, 4, 5).

Front

Which of the following is a Pythagorean triple? 9, 12, 14; 8, 15, 18; 7, 24, 25; 10, 20, 22

Back

7, 24, 25

Front

How can you determine if a set of lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

Which set of side lengths does not form a right triangle? 38, 80, 90; 16, 63, 65; 36, 77, 85; 14, 15, 29

Back

14, 15, 29

Front

If a = 3 feet, b = 8 feet, and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?

Back

10.44 feet

Front

What is the formula to find the diagonal of a rectangle?

Back

The formula to find the diagonal (d) of a rectangle with width (w) and length (l) is: d = √(w² + l²).

Front

A soccer field is a rectangle 90 meters wide and 120 meters long. What is the distance from one corner to the diagonally opposite corner?

Back

150 m

Front

What is the height of a cone if the radius is 5 cm and the slant height is 13 cm?

Back

Using the Pythagorean theorem, height (h) = √(slant height² - radius²) = √(13² - 5²) = 12 cm.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.