Intermediate Geometry explores the properties and relationships of shapes, sizes, and theorems in two and three dimensions.
The Pythagorean Theorem is a key geometric idea for right triangles. It also helps us find the distance between two points in a plane.
If a triangle has a right angle, then: \[ a^2 + b^2 = c^2 \] where \(a\) and \(b\) are legs, and \(c\) is the hypotenuse.
To find the distance between \((x_1, y_1)\) and \((x_2, y_2)\): \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
The theorem is useful in navigation, sports (measuring diagonals on fields), and computer graphics for pixel distances.
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Finding the shortest path between two points on a map.
Calculating the diagonal of a TV screen.
The Pythagorean Theorem helps us solve problems involving right triangles and distance.