Pythagorean Theorem + Applications

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

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

Back

To find the length of the hypotenuse in a right triangle, 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 the relationship between the sides of a right triangle?

Back

In a right triangle, the lengths of the sides must satisfy the Pythagorean Theorem. If a, b, and c are the lengths of the sides, then a² + b² = c², where c is the hypotenuse.

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. It is denoted as √x.

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

How can you determine if a set of numbers can represent the sides of a right triangle?

Back

To determine if a set of numbers can represent the sides of a right triangle, check if the largest number squared is equal to the sum of the squares of the other two numbers. This follows the Pythagorean Theorem.

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The formula to calculate the diagonal (d) of a rectangle with width (w) and height (h) is: d = √(w² + h²).

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 5² + 12² = 25 + 144 = 169, which equals 13².

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean Theorem.

Front

What is a right triangle?

Back

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