Pythagorean Review 2

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). Formula: a² + b² = c².

Front

What is a Pythagorean Triple?

Back

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

Front

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

Back

To find the length of the hypotenuse (c), use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

What is the distance formula in a coordinate plane?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

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

Back

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

Front

Does the set of numbers 5, 12, 13 represent a Pythagorean Triple?

Back

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

Front

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

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is the longest side.

Front

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

Back

Use the Pythagorean Theorem: Check if a² + b² = c², where c is the longest side.

Front

What is the length of the diagonal of a rectangle with sides 3 and 4?

Back

Using the distance formula: d = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

If the coordinates of point A are (1, 2) and point B are (4, 6), what is the distance between them?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.