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: a² + b² = c².

Front

In which type of triangle does the Pythagorean Theorem apply?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

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

Back

False.

Front

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

Back

Using the Pythagorean Theorem: b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8.

Front

What does 'c' represent in the Pythagorean Theorem?

Back

'c' represents the length of the hypotenuse, which is the side opposite the right angle.

Front

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

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289 = 17².