GVMS Practice for Retake 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). Formula: 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

What is a right triangle?

Back

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

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. For example, √9 = 3 because 3 x 3 = 9.

Front

If one side of a right triangle is 10 feet and the other side is 24 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(10² + 24²) = √(100 + 576) = √676 = 26 feet.

Front

What is the distance formula in coordinate geometry?

Back

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

Front

Can a triangle with sides 4, 5, and 6 be a right triangle?

Back

No, because it does not satisfy the Pythagorean Theorem: 4² + 5² ≠ 6².

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

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 27 feet, what is the length of the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 27²) = √(100 + 729) = √829, which is approximately 28.8 feet.