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). Formula: a² + b² = c².

Front

What is the formula for the Pythagorean Theorem?

Back

a² + b² = c²

Front

If one side of a right triangle is 8 and the other side is 15, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289, so c = √289 = 17.

Front

Does the set of numbers 9, 12, 15 represent a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

Find the length of the missing side if one side is 6 and the hypotenuse is 10.

Back

Using the Pythagorean Theorem: c² = a² + b², 10² = 6² + b², 100 = 36 + b², b² = 64, so b = 8.

Front

What is a right triangle?

Back

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

Front

If the lengths of the two legs of a right triangle are 5 and 12, what is the length of the hypotenuse?

Back

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

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 7, 24, and 25, does it form a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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