Pythagorean Theorem

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: c² = a² + b².

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

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

5 units (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

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

Use the Pythagorean Theorem: if the rectangle has width w and length l, the diagonal d can be found using d = √(w² + l²).

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

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

It can be used to determine distances, such as finding the height of a ladder against a wall or the diagonal distance across a rectangular field.

Area = (1/2) × base × height.