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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

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

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

In the Pythagorean Theorem, what are sides a and b called?

Back

Sides a and b are called the legs of the right triangle.

Front

What is the length of the hypotenuse if the legs of a right triangle are 6 cm and 8 cm?

Back

10 cm (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100; √100 = 10).

Front

What is the formula for finding the length of one leg of a right triangle if the hypotenuse and the other leg are known?

Back

The formula is: a = √(c² - b²) or b = √(c² - a²), where c is the hypotenuse and a and b are the legs.

Front

If a right triangle has a hypotenuse of 13 cm and one leg of 5 cm, what is the length of the other leg?

Back

12 cm (Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

Front

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

Back

The relationship is defined by the Pythagorean Theorem: c² = a² + b².

Front

Can the Pythagorean Theorem be used for obtuse or acute triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the length of the diagonal of a rectangle that is 90 meters wide and 120 meters long?

Back

150 meters (Using the Pythagorean Theorem: 90² + 120² = 8100 + 14400 = 22500; √22500 = 150).