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

In a right triangle, which side is the hypotenuse?

Back

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

Front

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

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

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

Back

8 cm (Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the hypotenuse.

Front

If a right triangle has sides of length 5 cm and 12 cm, what is the length of the hypotenuse?

Back

13 cm (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

In a right triangle, if one side is 8 cm and the hypotenuse is 10 cm, what is the length of the other side?

Back

6 cm (Using the Pythagorean Theorem: 10² = 8² + b²; 100 = 64 + b²; b² = 36; b = 6).

Front

What is the Pythagorean Theorem used for?

Back

It is used to determine the length of a side in a right triangle when the lengths of the other two sides are known.