Pythagorean Theorem Practice

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

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

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

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

If the hypotenuse of a right triangle is 10 cm and one side is 6 cm, how do you find the other side?

Back

Use the Pythagorean Theorem: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.

Front

If a right triangle has legs of lengths 8 cm and 15 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(8² + 15²) = √(64 + 225) = √289 = 17 cm.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.