Pythagorean Flashcard - applying and coordinate grid K&K

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.

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

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean Theorem.

To determine if a triangle with side lengths a, b, and c is a right triangle, check if a² + b² = c² holds true, where c is the longest side.

The Pythagorean Theorem provides a relationship between the lengths of the sides of a right triangle, allowing us to find the length of one side if the lengths of the other two sides are known.

To find the width of a screen given the diagonal (d) and height (h), use the Pythagorean Theorem: w = √(d² - h²), where w is the width.

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

A coordinate grid is a two-dimensional plane formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis), used to locate points using ordered pairs (x, y).

To apply the Pythagorean Theorem to real-world problems, identify the right triangle formed by the situation, label the sides, and use the theorem to find the unknown side length.