IAG: Pythagorean Theorem Applications

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

How can you determine if three side lengths form a right triangle?

Back

To determine if three side lengths (a, b, c) form a right triangle, check if the Pythagorean Theorem holds true: a² + b² = c², where c is the longest side.

Front

If the side lengths are 13, 81, and 80, do they form a right triangle?

Back

No, because 13² + 80² = 169 + 6400 = 6569, which is not equal to 81² = 6561.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane can be calculated using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

If John walks 6 blocks south and 8 blocks east, how far is he from the starting point?

Back

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

Front

What is the width of a computer monitor if the diagonal is 27 inches and the height is 15 inches?

Back

Using the Pythagorean Theorem: w = √(27² - 15²) = √(729 - 225) = √504 ≈ 22 inches.

Front

Do the segment lengths 15, 12, and 9 form a right triangle?

Back

Yes, because 9² + 12² = 81 + 144 = 225 = 15².

Front

If Jane walks 6 blocks east and Miguel walks 8 blocks north, how far apart are their schools?

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.