Geometric Mean and Pythagorean Theorem Flashcard

Front

What is the geometric mean of two numbers a and b?

Back

The geometric mean is defined as the square root of the product of the two numbers: √(a * b).

Front

What is the formula for 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): c² = a² + b².

Front

Calculate the geometric mean of 4 and 16.

Back

The geometric mean of 4 and 16 is 8.

Front

In a right triangle, if one leg is 9 and the hypotenuse is 15, what is the length of the other leg?

Back

The length of the other leg is 12.

Front

How can you determine if a triangle with sides 10, 24, and 26 is a right triangle?

Back

Use the Pythagorean Theorem: check if 10² + 24² = 26². Since 100 + 576 = 676, it is a right triangle.

Front

What are the conditions for three lengths to form a right triangle?

Back

The lengths must satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

If the geometric mean of two numbers is 6 and one number is 3, what is the other number?

Back

The other number is 12.

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

It is a right triangle because 5² + 12² = 13².

Front

List a set of side lengths that can form a right triangle.

Back

5, 12, 13; 6, 8, 10; 7, 24, 25; 9, 40, 41 are all valid sets.

Front

What is the geometric mean of 9 and 25?

Back

The geometric mean is 15.