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). Formula: a² + b² = c².

Front

What is the formula for finding the hypotenuse?

Back

a² + b² = c².

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, so c = √25 = 5).

Front

What is the length of the missing side if the hypotenuse is 10 and one side is 6?

Back

8 (Using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, b² = 64, b = √64 = 8).

Front

What do the letters a, b, and c represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of a right triangle, and 'c' represents the length of the hypotenuse.

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If the lengths of the sides satisfy the equation a² + b² = c², then the triangle is a right triangle.

Front

What is the length of the missing side if the hypotenuse is 13 and one side is 5?

Back

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

Front

If a triangle has sides of lengths 8 and 15, what is the length of the hypotenuse?

Back

17 (Using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289, so c = √289 = 17).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If the hypotenuse is 25 and one side is 24, what is the length of the other side?

Back

7 (Using the Pythagorean Theorem: 24² + b² = 25², so 576 + b² = 625, b² = 49, b = √49 = 7).