Polygons

1. Polygons Section 1.5

2. A polygonis a closed geometric figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others.

3. You classify polygons by the number of sides they have. • A polygon with three sides is a triangle. • The symbol for triangle is ∆. • A polygon with four sides is a quadrilateral. • A polygon with five sides is a pentagon. • A polygon with six sides is a hexagon. • A polygon with seven sides is a heptagon. • A polygon with eight sides is a octagon. • A polygon with nine sides is a nonagon. • A polygon with ten sides is a decagon.

4. A polygon with eleven sides is a undecagon. • A polygon with twelve sides is a dodecagon. Each line segment is called a side of the polygon. Each endpoint where the sides meet is called a vertexof the polygon. If two sides share a common vertex, then they are consecutivesides. If two vertices of a polygon share a common side, they are consecutivevertices.

5. When referring to a specific polygon, list in succession the capital letters representing consecutive vertices. You may start at any vertex and go in either order, but the vertices must then be listed successively.

6. Congruence • If two segments or two angles have the same measure, they are called congruent. The symbol for congruent is . • We use tick marks to show segments are congruent and arcs to show angles are congruent.

7. U E F G N O • If two polygons are congruent, then corresponding sides are equal and corresponding angles are equal.

8. In addition to classifying polygons by the number of sides, you may use words to describe lengths of segments and the measure of angles. • A polygon is an equilateral polygon if and only if all sides are congruent. • A polygon is an equilateral polygon if and only if all angles are congruent. • A polygon is a regular polygon if and only if all angles and all sides are congruent.