British Flag Theorem
In Euclidian Geometry, the British flag theorem states that if a point is chosen inside rectangle , then . The theorem is called the British flag theorem due to the similarities between the British flag and a diagram of the points (shown below):
This is also true when point is located outside or on the boundary of , and even when is located in a Euclidian space where is embedded.
We build right triangles by drawing a line through perpendicular to two sides of the rectangle, as shown below. Both and are rectangles. Applying the Pythagorean Theorem to each of the four right triangles in the diagram, we have So, we have From rectangles and , we have and , so the expressions above for and are equal, as desired.