Polygon vocabulary

Learning Objectives Define and identify key polygon vocabulary including vertex, side, diagonal, convex, concave, and regular. Classify polygons by their number of sides, from triangles to dodecagons. Differentiate between convex and concave polygons based on their interior angles and diagonals. Distinguish between equilateral, equiangular, and regular polygons. Apply the Polygon Interior Angle Sum Theorem to find the sum of the interior angles of any convex polygon. Apply the Polygon Exterior Angle Sum Theorem. Calculate the measure of a single interior or exterior angle of a regular polygon. Ever wonder why stop signs are octagons and beehives are made of hexagons? 🛑🐝 The specific vocabulary of polygons holds the key to understanding the geometry that shapes our world....

TermDefinitionExample PolygonA closed plane figure formed by three or more coplanar line segments called sides. Each side intersects exactly two other sides, one at each endpoint, so that no two sides with a common endpoint are collinear.A triangle, a square, a pentagon, and a hexagon are all polygons. DiagonalA line segment that connects two non-consecutive vertices of a polygon.In a square ABCD, the segments AC and BD are diagonals. A triangle has no diagonals. Convex vs. Concave PolygonA polygon is CONVEX if no line that contains a side of the polygon contains a point in the interior of the polygon. A polygon is CONCAVE if it has at least one interior angle greater than 180° (a reflex angle), creating a 'dent' or 'cave'.A rectangle is convex. A five-pointed star is...

Polygon Interior Angle Sum Theorem S = (n-2) \cdot 180^\circ Use this formula to find the sum (S) of the measures of the interior angles of any convex polygon with 'n' sides. Interior Angle of a Regular Polygon \text{Interior Angle} = \frac{(n-2) \cdot 180^\circ}{n} Use this formula to find the measure of a single interior angle of a REGULAR polygon with 'n' sides. Do not use for irregular polygons. Polygon Exterior Angle Sum Theorem S_{ext} = 360^\circ The sum of the measures of the exterior angles (one at each vertex) of ANY convex polygon is always 360°, regardless of the number of sides. Exterior Angle of a Regular Polygon \text{Exterior Angle} = \frac{360^\circ}{n} Use this formula to find the measure of a single exterior angle of a R...