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 the hypotenuse in a right triangle?

Back

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

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

The length of the hypotenuse is 13 cm, calculated using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, so c = √169 = 13.

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Front

What is the formula for the Pythagorean Theorem?

Back

c² = a² + b².

Front

If the hypotenuse is 10 cm and one side is 6 cm, what is the length of the other side?

Back

The length of the other side is 8 cm, calculated as follows: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8.

Front

What does 'a' and 'b' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs (the sides that form the right angle) of the right triangle.

Front

In a right triangle, if one leg is 9 cm and the hypotenuse is 15 cm, what is the length of the other leg?

Back

The length of the other leg is 12 cm, calculated as follows: 15² = 9² + b², so 225 = 81 + b², thus b² = 144, and b = √144 = 12.

Front

True or False: The Pythagorean Theorem can be used to find the distance between two points in a coordinate plane.

Back

True.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The square of the hypotenuse is equal to the sum of the squares of the other two sides.