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). It is expressed as c² = a² + b².

Front

What is a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (a and b) and the hypotenuse (c). The hypotenuse is the longest side, opposite the right angle.

Front

If one leg of a right triangle is 3 inches and the other leg is 4 inches, what is the length of the hypotenuse?

Back

5 inches (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

Can the lengths 8, 15, and 17 form a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289, and 17² = 289.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

If the hypotenuse is 10 inches and one leg is 6 inches, what is the length of the other leg?

Back

8 inches (using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8).

Front

What does it mean for a set of numbers to represent a right triangle?

Back

It means that the numbers can be the lengths of the sides of a triangle that satisfies the Pythagorean Theorem.

Front

Which of the following sets of numbers can form a right triangle: 5, 12, 13 or 4, 5, 6?

Back

5, 12, 13 can form a right triangle because 5² + 12² = 25 + 144 = 169, and 13² = 169.

Front

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

Back

The sum of the squares of the two legs equals the square of the hypotenuse.