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Lesson 1.1: POLYGONLesson 1.2 TrianglesLesson 1.3 QuadrilateralsWeek 1 and Week 2Math 139 – 1Solid Mensuration
A polygonis a closed plane figure that is joined by line segments. A polygon may also be defined as a union of line segments such that:
Reference: Solid Mensuration by Richard Earnhart
Parts of a PolygonExterior AngleVertexSide or EdgeDiagonalInterior AngleReference: Solid Mensuration by Richard Earnhart
Types of PolygonRegular Polygon.In a regular polygon, all angles are equal and all sides are of the same length. Regular polygons are both equiangular and equilateral.Equiangular Polygon.A polygon is equiangular if all of its angles are congruent.Equilateral Polygon.A polygon is equilateral if all of its sides are equal.Irregular Polygon.A polygon that is neither equiangular nor equilateral is said to be an irregular polygon.Reference: Solid Mensuration by Richard Earnhart
TYPES OF POLYGONConvex PolygonEvery interior angle of a convex polygon is less than 180°. If a line is drawn through the convex polygon, the line will intersect at most two sides.Reference: Solid Mensuration: Understanding the 3-D Space by Richard T. Earnhart
TYPES OF POLYGONConcave PolygonA concave polygon has at least one interior angle that measures more than 180°. If a line is drawn through a concave polygon, the line may intersect more than two sides.Reference: Solid Mensuration: Understanding the 3-D Space by Richard T. Earnhart
NAMING OF POLYGONReference: Solid Mensuration by Richard Earnhart
Reference: Solid Mensuration by Richard Earnhart
Reference: Solid Mensuration by Richard Earnhart
Reference: Solid Mensuration by Richard Earnhart
Reference: Solid Mensuration by Richard Earnhart
We say that two polygons are similarif their corresponding interior angles are congruent and their corresponding sides are proportional.By ratio and proportion,Similar Polygons Reference: Solid Mensuration by Richard Earnhart
.Reference: Solid Mensuration by Richard Earnhart
ExamplesPerimeter: Central Angle: Apothem: no. of sides s/2θ/2aReference: Solid Mensuration by Richard Earnhart
No. of Diagonals:Interior Angle:Sum of Interior Angle:AREAReference: Solid Mensuration by Richard Earnhart
Example 1, page 8Find the area of a regular nonagon with a side that measures 3 units. Also find the number of diagonals and the sum of its interior angles.

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