Pythagorean Theorem Review

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

What is the hypotenuse in a right triangle?

Back

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

Front

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

Back

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

Front

Which of the following sets of numbers can be the sides of a right triangle? 5, 12, 13 or 8, 15, 17?

Back

Both sets can be the sides of a right triangle. (5² + 12² = 13² and 8² + 15² = 17²).

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 other two sides.

Front

If a right triangle has sides 6 and 8, what is the length of the hypotenuse?

Back

10 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so c = √100 = 10).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Can a triangle with sides 7, 24, and 25 be a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, which is equal to 25².

Front

What is the length of the missing side if one side is 12 and the hypotenuse is 13?

Back

5 (Using the Pythagorean Theorem: 13² = 12² + b², so 169 = 144 + b², thus b² = 25, and b = 5).

Front

What is the definition of a right triangle?

Back

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