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 the formula to find the hypotenuse of a right triangle?

Back

The formula to find the hypotenuse (c) of a right triangle is c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

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

Back

The hypotenuse is 5, calculated using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the relationship between the sides of a right triangle?

Back

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

Back

The length of the other leg is 8, calculated using the formula: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem (a² + b² ≠ c²), it is not a right triangle.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides a, b, and c such that a² + b² = c², then the triangle is a right triangle.

Front

How can the Pythagorean Theorem be applied in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the distance between two points, construction, navigation, and in various fields of engineering.

Front

What is the Pythagorean triple?

Back

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

Front

What is the length of the hypotenuse if the legs of a right triangle are 5 and 12?

Back

The length of the hypotenuse is 13, calculated as c = √(5² + 12²) = √(25 + 144) = √169 = 13.