Polygons Lesson 3 4 Polygons 1 Polygons Definition

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Polygons Lesson 3 -4: Polygons 1

Polygons Lesson 3 -4: Polygons 1

Polygons Definition: A closed figure formed by a finite number of coplanar segments so

Polygons Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. These figures are not polygons Lesson 3 -4: Polygons These figures are polygons 2

Classifications of a Polygon Convex: No line containing a side of the polygon contains

Classifications of a Polygon Convex: No line containing a side of the polygon contains a point in its interior Concave: A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon. Lesson 3 -4: Polygons 3

Classifications of a Polygon Regular: A convex polygon in which all interior angles have

Classifications of a Polygon Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length Irregular: Two sides (or two interior angles) are not congruent. Lesson 3 -4: Polygons 4

Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon

Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon 12 sides n sides Dodecagon n-gon Lesson 3 -4: Polygons 5

Convex Polygon Formulas…. . Diagonals of a Polygon: A segment connecting nonconsecutive vertices of

Convex Polygon Formulas…. . Diagonals of a Polygon: A segment connecting nonconsecutive vertices of a polygon For a convex polygon with n sides: The sum of the interior angles is The measure of one interior angle is The sum of the exterior angles is The measure of one exterior angle is Lesson 3 -4: Polygons 6

Examples…. . 1. Sum of the measures of the interior angles of a 11

Examples…. . 1. Sum of the measures of the interior angles of a 11 -gon is (n – 2)180° (11 – 2)180 ° 1620 2. The measure of an exterior angle of a regular octagon is 3. The number of sides of regular polygon with exterior angle 72 ° is 4. The measure of an interior angle of a regular polygon with 30 sides 5. The number of sides of regular polygon with interior angle 172 ° is Lesson 3 -4: Polygons 7