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

Back

To find the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

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: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the longest side of a right triangle called?

Back

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

Front

How do you cancel out the square when solving using the Pythagorean Theorem?

Back

You cancel out the square by taking the square root of both sides.

Front

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

Back

Use the formula: b = √(c² - a²). Here, b = √(10² - 6²) = √(100 - 36) = √64 = 8 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 8 cm and the hypotenuse is 10 cm, what is the length of the other leg?

Back

The length of the other leg is 6 cm, calculated using the Pythagorean Theorem: a = √(c² - b²) = √(10² - 8²) = √(100 - 64) = √36 = 6.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.