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: c² = a² + b².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²).

Front

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

Back

The length of the hypotenuse is 5 cm, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem.

Front

How do you find a missing leg of a right triangle?

Back

To find a missing leg (a or b), rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

What is the Pythagorean Triplet?

Back

A Pythagorean Triplet consists of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, such as (3, 4, 5) or (5, 12, 13).

Front

If the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

The length of the other leg is 8 cm, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

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.