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 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 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the length of a missing side in a right triangle?

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c², where a and b are the legs and c is the hypotenuse.

Front

If the hypotenuse is 13 cm and one leg is 5 cm, how do you find the other leg?

Back

Use the formula: b² = c² - a²; b² = 13² - 5²; b² = 169 - 25; b² = 144; b = 12 cm.

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

In a right triangle, if one leg is 9 cm and the hypotenuse is 15 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² = c² - b²; a² = 15² - 9²; a² = 225 - 81; a² = 144; a = 12 cm.

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

How can you determine if a triangle is a right triangle?

Back

A triangle is a right triangle if the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides.

Front

What is the area of a right triangle with legs of 5 cm and 12 cm?

Back

Area = (1/2) * base * height = (1/2) * 5 * 12 = 30 cm².