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 does the letter 'c' represent in a right triangle?

Back

In a right triangle, 'c' represents the length of the hypotenuse, which is the side opposite the right angle and is always the longest side.

Front

If one side of a right triangle is 8 and the other side is 6, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 6² = 64 + 36 = 100. Therefore, c = √100 = 10.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

In a right triangle, which side is always the longest?

Back

The hypotenuse (side c) is always the longest side in a right triangle.

Front

If the hypotenuse is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: 13² = 5² + b². Therefore, 169 = 25 + b², so b² = 144, and b = √144 = 12.

Front

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

Back

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

Front

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

Back

True. The Pythagorean Theorem is applicable only to right triangles.

Front

If a right triangle has sides of length 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225. Therefore, c = √225 = 15.

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 (a and b) equals the square of the longest side (c): a² + b² = c².