Inside a Regular Polygon

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 9 of 61.

A diagonal that skips one vertex of a regular polygon cuts off a triangle whose two sides are sides of the polygon. In square ABCD, the diagonal AC makes triangle ABC with AB = BC, so the triangle is isosceles.

$Square ABCD with the diagonal AC$

The base angles of an isosceles triangle are equal, and here the angle between them is the square's corner, 90°. So 2 × b + 90 = 180, which gives each base angle 45°. The diagonal of a square cuts its corner exactly in half.

In other regular polygons it takes two steps: first the polygon's angle from Angles in a polygon, then the base angles from Isosceles triangle.