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 longest side of a right triangle called?

Back

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

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

The hypotenuse is 5 cm, calculated using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5.

Front

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

Back

The length of the other leg is 8 cm, calculated using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8.

Front

What is the formula to find the hypotenuse in a right triangle?

Back

The formula to find the hypotenuse (c) is c = √(a² + b²).

Front

What is the formula to find a leg in a right triangle if the hypotenuse and the other leg are known?

Back

The formula to find a leg (a) is a = √(c² - b²).

Front

In a right triangle, if the legs are 5 cm and 12 cm, what is the hypotenuse?

Back

The hypotenuse is 13 cm, calculated as: 5² + 12² = 25 + 144 = 169, so c = √169 = 13.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The relationship is that the sum of the squares of the two legs equals the square of the hypotenuse: a² + b² = c².

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem is specific to right triangles only.