Lesson 1-6 Polygons Lesson 3-4: Polygons.

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Presentation transcript:

Lesson 1-6 Polygons Lesson 3-4: Polygons

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 Lesson 3-4: Polygons

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

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

What is this shape? Lesson 3-4: Polygons

What is this shape? Lesson 3-4: Polygons

What is this shape? Lesson 3-4: Polygons

What is this shape? Lesson 3-4: Polygons

What is the shape? Lesson 3-4: Polygons

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

Perimeter: Given P=144, find the value of x and the length of each side. Lesson 3-4: Polygons

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

Examples….. Sum of the measures of the interior angles of a 11-gon is 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