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

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

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

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

How do you find the length of one side of a right triangle if you know the hypotenuse and one other side?

Back

You can rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Using the distance formula: d = √((x2 - x1)² + (y2 - y1)²) = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is d = √((x2 - x1)² + (y2 - y1)²), which calculates the distance between two points in a coordinate plane.

Front

In a right triangle, if one leg is 6 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the side opposite the 30° angle is the shortest.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.