7.1 Pythagorean Theorem & Converse

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 Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c². Examples include (3, 4, 5) and (5, 12, 13).

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25 = 5².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you determine if a set of numbers is a Pythagorean Triple?

Back

To determine if a set of numbers is a Pythagorean Triple, check if the square of the largest number equals the sum of the squares of the other two numbers.

Front

Find the value of x if the sides of a right triangle are 6 and 8. What is x?

Back

x = 10, because 6² + 8² = 36 + 64 = 100, and √100 = 10.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

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

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

Front

If the lengths of the two legs of a right triangle are 9 and 12, what is the length of the hypotenuse?

Back

The hypotenuse is 15, because √(9² + 12²) = √(81 + 144) = √225 = 15.