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

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies to 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

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

Front

What is the square root of 25?

Back

5.

Front

If a = 5 and b = 12, what is the length of c in a right triangle?

Back

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

Front

What is the opposite of squaring a number?

Back

Square root.

Front

In the equation a² + b² = c², what does 'c' represent?

Back

'c' represents the length of the hypotenuse of a right triangle.

Front

If b = 35 and c = 37, what is the value of a?

Back

12 (Using the Pythagorean Theorem: a² + 35² = 37²; a² + 1225 = 1369; a² = 144; a = 12).

Front

Can you find right triangles in real life applications?

Back

Yes, right triangles can be found in various real-life applications, such as in construction and architecture.

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

You can rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).