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 for the Pythagorean Theorem?

Back

The formula is a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

What is the longest side of a right triangle called?

Back

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

Front

If a = 3 and b = 4, what is c in the Pythagorean Theorem?

Back

c = 5, because 3² + 4² = 9 + 16 = 25, and √25 = 5.

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 (legs) equals the square of the longest side (hypotenuse).

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 5² + 12² = 25 + 144 = 169, which is 13².

Front

How do you find the length of the diagonal of a rectangle using the Pythagorean Theorem?

Back

Use the lengths of the rectangle as the two legs of a right triangle. The diagonal is the hypotenuse: d = √(length² + width²).

Front

In a right triangle, if one leg is 6 and the hypotenuse is 10, what is the length of the other leg?

Back

The other leg is 8, because 6² + b² = 10², so 36 + b² = 100, and b² = 64, thus b = 8.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (3, 4, 5).