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). Formula: 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 6 and the other leg is 8, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the length of a leg in a right triangle if the hypotenuse and one leg are known?

Back

The formula is a² = c² - b² or b² = c² - a², where c is the hypotenuse and a and b are the legs.

Front

In a right triangle, if the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Back

12 (Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

If a right triangle has legs of lengths 9 and 12, what is the length of the hypotenuse?

Back

15 (Using the Pythagorean Theorem: 9² + 12² = c²; 81 + 144 = c²; 225 = c²; c = 15).

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

Front

If the hypotenuse is 25 and one leg is 20, what is the length of the other leg?

Back

15 (Using the Pythagorean Theorem: 20² + b² = 25²; 400 + b² = 625; b² = 225; b = 15).

Front

What is the value of c if a = 3 and b = 4 in a right triangle?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5).