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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

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 15 m and the other leg is 20 m, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 15² + 20²; c² = 225 + 400; c² = 625; c = 25 m.

Front

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

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

How do you solve for a side when you know the hypotenuse and one leg?

Back

Rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

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 satisfy the Pythagorean Theorem: 3² + 4² = 5².

Front

What is the value of the hypotenuse if one leg is 8 m and the other leg is 6 m?

Back

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

Front

What is the Pythagorean triple?

Back

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

Front

What is the significance of the right angle in the Pythagorean Theorem?

Back

The right angle is crucial because the Pythagorean Theorem only applies to right triangles.