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 can be expressed as: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one leg of a right triangle is 12 and the other leg is 9, what is the length of the hypotenuse?

Back

The hypotenuse is 15, calculated using the Pythagorean Theorem: c² = 12² + 9² = 144 + 81 = 225, thus c = √225 = 15.

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

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

Back

Yes, they can form a right triangle because 8² + 15² = 64 + 225 = 289 = 17².

Front

If the hypotenuse of a right triangle is 50 and one leg is 30, what is the length of the other leg?

Back

The length of the other leg is 40, calculated using the Pythagorean Theorem: 50² = 30² + b², thus 2500 = 900 + b², so b² = 1600, and b = √1600 = 40.

Front

What is the formula to find the hypotenuse in a right triangle?

Back

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

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

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

Back

The hypotenuse is 10, calculated using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, thus 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.