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

If a = 9 and b = 40, what is the length of the hypotenuse (c)?

Back

Using the Pythagorean Theorem: c = √(a² + b²) = √(9² + 40²) = √(81 + 1600) = √1681 = 41.

Front

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

Back

To find the length of a missing side, use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to solve for the missing side.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The diagonal (d) of a rectangle can be calculated using the Pythagorean Theorem: d = √(length² + width²).

Front

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

Back

Using the Pythagorean Theorem: d = √(3² + 6²) = √(9 + 36) = √45 ≈ 6.7 feet.

Front

What are the side lengths of a right triangle?

Back

A set of side lengths forms a right triangle if they satisfy the Pythagorean Theorem: a² + b² = c². For example, 5, 12, and 13 are the lengths of a right triangle.

Front

How can you determine if three side lengths form an acute triangle?

Back

For three sides a, b, and c to form an acute triangle, the following must be true: a² + b² > c² (where c is the longest side).

Front

How can you determine if three side lengths form an obtuse triangle?

Back

For three sides a, b, and c to form an obtuse triangle, the following must be true: a² + b² < c² (where c is the longest side).

Front

What is the difference between acute, obtuse, and right triangles?

Back

An acute triangle has all angles less than 90 degrees, a right triangle has one angle equal to 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.