Chapter 6 Section 6.1 Polygons.

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Presentation transcript:

Chapter 6 Section 6.1 Polygons

180o 3x + 34 + 53 = 180 3x + 87 = 180 3x = 93 x = 31 Equilateral Equiangular

Examples of Polygons Identify, Name, and Describe Polygons Definition Definition Polygon A polygon is a plane figure that is formed by three or more segments called sides, such that no two sides with a common endpoint are collinear, and each side intersects exactly two other sides, one at each endpoint. Each endpoint is called a vertex of the polygon Examples of Polygons

No: All sides must be straight Identify, Name, and Describe Polygons No: All sides must be straight No: All sides must be straight Yes

Identify, Name, and Describe Polygons Names Names Polygon Names A polygons name depends on the number of sides it has # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon # of Sides Name 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon N N-gon

Non-Convex/Concave: A polygon that is not convex Identify, Name, and Describe Polygons Descriptions Descriptions Describing Polygons A polygons description depends on its shape Convex: No line that contains a side of the polygon contains a point in the interior of the polygon Non-Convex/Concave: A polygon that is not convex Examples

Hexagon Concave Heptagon Heptagon Concave Convex Identify, Name, and Describe Polygons Hexagon Concave Heptagon Heptagon Concave Convex

Identify, Name, and Describe Polygons Heptagon BCDEFGA DEFGABC

Identify, Name, and Describe Polygons C, D, E, F

Identify, Name, and Describe Polygons

Sum interior angles of a quadrilateral Theorem Theorem 6.1 Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360o mH + mG + mF + mE = 360o

Sum interior angles of a quadrilateral (x + 15) + (x + 15) + (2x) + (2x) = 360 6x + 30 = 360 6x = 330 x = 55

Sum interior angles of a quadrilateral (5x - 15) + (3x - 1) + (4x + 34) + (5x - 15) = 360 17x + 3 = 360 17x = 357 x = 21

Sum interior angles of a quadrilateral (4x - 15) + (5x + 11) + (6x + 19) + (5x + 5) = 360 20x + 20 = 360 20x = 340 x = 17

HW #66 Pg 325-328 12-20 Even, 21-23, 24-38 Even 42-52 Even