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Lesson 3-4

Polygons. Lesson 3-4. 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. These figures are polygons. Classifications of a Polygon. Convex:.

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Lesson 3-4

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  1. Polygons Lesson 3-4 Lesson 3-4: Polygons

  2. 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 arenot polygons These figures are polygons Lesson 3-4: Polygons

  3. 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

  4. 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

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

  6. 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

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

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