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 are the sides of a right triangle called?

Back

In a right triangle, the two shorter sides are called 'legs' (a and b), and the longest side opposite the right angle is called the 'hypotenuse' (c).

Front

Which side is always opposite the right angle in a right triangle?

Back

The hypotenuse is always opposite the right angle in a right triangle.

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

True or False: The hypotenuse is the shortest side of a right triangle.

Back

False. The hypotenuse is the longest side of a right triangle.

Front

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

Back

To find a missing leg (a or b), rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

If the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8 cm.

Front

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

Back

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

Front

In a right triangle, if both legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Front

If the lengths of the legs of a right triangle are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13 cm.