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 is the formula to find the hypotenuse in a right triangle?

Back

The formula to find the hypotenuse (c) is: c = √(a² + b²).

Front

In a right triangle, which side is the longest?

Back

The longest side of a right triangle is called the hypotenuse.

Front

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

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

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

Back

True.

Front

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

Back

'a' and 'b' represent the lengths of the two legs of a right triangle.

Front

If the hypotenuse is 13 and one leg is 5, how do you find the other leg?

Back

Use the formula: b = √(c² - a²). Here, b = √(13² - 5²) = √(169 - 25) = √144 = 12.

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

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25 = 5².

Front

What is the value of c if a = 9 and b = 12?

Back

c = √(9² + 12²) = √(81 + 144) = √225 = 15.