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 is a right triangle?

Back

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

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

Which of the following is NOT a perfect square: 49, 81, 111, 144?

Back

111 is NOT a perfect square.

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).

Front

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

Back

The hypotenuse is 5, calculated as c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Front

Estimate the square root of 10. Is it between 3 and 4?

Back

Yes, the square root of 10 is between 3 and 4, closer to 3.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If the lengths of the two legs of a right triangle are 6 and 8, what is the length of the hypotenuse?

Back

The hypotenuse is 10, calculated as c = √(6² + 8²) = √(36 + 64) = √100 = 10.