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 can be expressed as a² + b² = c².

Front

In a right triangle, which side is the longest?

Back

The longest side in a right triangle is the hypotenuse, which is opposite the right angle.

Front

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

Back

Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5 feet.

Front

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

Back

The relationship is defined by the Pythagorean theorem, which states that the sum of the squares of the two shorter sides equals the square of the longest side.

Front

How do you find the length of a missing side in a right triangle?

Back

To find a missing side, use the Pythagorean theorem: if you know the lengths of two sides, you can rearrange the formula a² + b² = c² to solve for the missing side.

Front

What is the formula for calculating the diagonal of a rectangle?

Back

The formula for calculating the diagonal (d) of a rectangle is d = √(width² + height²).

Front

If a television screen is 3 feet tall and 6 feet wide, what is the diagonal size?

Back

Using the formula for the diagonal: d = √(6² + 3²) = √(36 + 9) = √45 ≈ 6.7 feet.

Front

What does it mean if a side of a triangle is labeled as 'a' in the Pythagorean theorem?

Back

In the context of the Pythagorean theorem, 'a' represents one of the two shorter sides of a right triangle.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is significant because it is the longest side and is used in the Pythagorean theorem to relate the lengths of the other two sides.

Front

Can the Pythagorean theorem be used for non-right triangles?

Back

No, the Pythagorean theorem only applies to right triangles.