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 a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

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

Back

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

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

The sides 5, 12, and 13 form a right triangle because they satisfy the Pythagorean Theorem: 5² + 12² = 13².

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

If the hypotenuse of a right triangle is 10 cm and one leg is 6 cm, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + 6² = 10²; a² + 36 = 100; a² = 64; a = 8 cm.

Front

What is a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c that satisfy the Pythagorean Theorem: a² + b² = c².