Pythagorean Theorem Mixed Review/Real Numbers

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

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as sides a and b in the Pythagorean Theorem.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction. It is a non-repeating, non-terminating decimal.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

The hypotenuse is 5, calculated using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so √25 = 5.

Front

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

Back

Yes, they do. 5² + 12² = 25 + 144 = 169, and √169 = 13.

Front

What is the distance from the wall to the base of a ladder that is 13 ft long and touches a wall 12 ft high?

Back

The distance is 5 ft, calculated using the Pythagorean Theorem: 12² + x² = 13², so x = 5.

Front

What is the square root of 169?

Back

The square root of 169 is 13.

Front

What is the definition of a whole number?

Back

A whole number is a non-negative integer, including zero (0, 1, 2, 3, ...).

Front

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

Back

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.