TEK 8.6C & 8.7C 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

How do you calculate the length of the diagonal of a rectangle?

Back

To calculate the length of the diagonal (d) of a rectangle with length (l) and width (w), use the Pythagorean Theorem: d = √(l² + w²).

Front

If a right triangle has sides of lengths 6 cm and 8 cm, what is the length of the hypotenuse?

Back

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

Front

Which of the following sets of lengths can represent the sides of a right triangle? 5 cm, 12 cm, 13 cm?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the relationship between the areas of squares formed on the sides of a right triangle?

Back

The sum of the areas of the squares on the two shorter sides is equal to the area of the square on the hypotenuse.

Front

What is the length of the diagonal of a rectangle with dimensions 8.5 inches and 11 inches?

Back

Using the Pythagorean Theorem: d = √(8.5² + 11²) = √(72.25 + 121) = √193.25 ≈ 13.9 inches.

Front

Can the lengths 4 cm, 6 cm, and 10 cm form a right triangle?

Back

No, because 4² + 6² = 16 + 36 = 52, which is not equal to 10² (100).

Front

What is the length of the diagonal of a rectangular frame with a length of 15 inches and a width of 8 inches?

Back

Using the Pythagorean Theorem: d = √(15² + 8²) = √(225 + 64) = √289 = 17 inches.

Front

What does it mean for a triangle to be a right triangle?

Back

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

Front

What is the formula for the area of a square?

Back

The area (A) of a square is calculated as A = side², where 'side' is the length of one side of the square.