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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula is a² + b² = c², where c is the length of the hypotenuse.

Front

If one side of a right triangle is 5 cm and the other side is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.

Front

Can a triangle with sides 8, 15, and 17 be classified as a right triangle?

Back

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

Front

What is a right triangle?

Back

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

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, and 25² = 625.

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

If a triangle has sides of lengths 10, 40, and 41, is it a right triangle?

Back

Yes, because 10² + 40² = 100 + 1600 = 1700, and 41² = 1681.

Front

What is the converse of the Pythagorean Theorem?

Back

If a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.