Regular and irregular polygons

Learning Objectives Define polygon, regular polygon, and irregular polygon. Classify polygons as regular or irregular based on their side lengths and interior angles. Differentiate between convex and concave polygons. Calculate the sum of the interior angles of any convex polygon using the appropriate formula. Calculate the measure of a single interior angle of a regular polygon. Calculate the measure of a single exterior angle of a regular polygon. Apply polygon properties to solve for unknown variables in geometric figures. Ever wonder why a honeycomb is made of perfect hexagons and a stop sign is always an octagon? 🐝🛑 Let's explore the precise world of polygons that shape our world! This tutorial will introduce you to the classification of polygons, focusing on...

TermDefinitionExample PolygonA closed, two-dimensional figure formed by three or more straight line segments (sides) that meet only at their endpoints (vertices).A triangle, a square, a pentagon. Regular PolygonA polygon that is both equilateral (all sides are equal in length) and equiangular (all interior angles are equal in measure).A square is a regular polygon because it has 4 equal sides and 4 equal 90° angles. An equilateral triangle is also a regular polygon. Irregular PolygonA polygon that is not regular. At least one side has a different length, or at least one angle has a different measure.A rectangle (that is not a square) is irregular because its adjacent sides are not equal. A scalene triangle is irregular because its sides and angles are all different. Convex PolygonA polygo...

Sum of Interior Angles of a Convex Polygon S = (n - 2) * 180° Use this formula to find the total measure of all interior angles in any convex polygon, where 'n' is the number of sides. Measure of a Single Interior Angle of a Regular Polygon A = ((n - 2) * 180°) / n Use this formula ONLY for regular polygons to find the measure of one interior angle. It's the total sum divided by the number of angles (n). Sum of Exterior Angles of a Convex Polygon S_ext = 360° The sum of the exterior angles of ANY convex polygon is always 360°, regardless of the number of sides. Measure of a Single Exterior Angle of a Regular Polygon E = 360° / n Use this formula to quickly find the measure of one exterior angle of a regular polygon, where 'n' is the n...