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 is expressed as a² + b² = c².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If one leg of a right triangle is 3 feet and the other leg is 4 feet, what is the length of the hypotenuse?

Back

5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

Do the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a side, rearrange the formula: a² = c² - b² or b² = c² - a².

Front

In a right triangle, if the hypotenuse is 10 feet and one leg is 6 feet, what is the length of the other leg?

Back

8 feet (using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64; √64 = 8).

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles is exactly 90 degrees.

Front

What is the relationship between the sides in the Pythagorean Theorem?

Back

The relationship is expressed as a² + b² = c², where c is the hypotenuse.

Front

If a right triangle has legs of lengths 8 and 15, what is the length of the hypotenuse?

Back

17 feet (using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289; √289 = 17).

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.