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Understanding Polygon Angle-Sum Theorems in Geometry

Learn how to find the sum of interior and exterior angles in polygons using relevant formulas and examples. Explore the Polygon Sum Theorem and its application in various types of polygons.

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Understanding Polygon Angle-Sum Theorems in Geometry

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  1. Chapter 6:Polygons and Quadrilaterals

  2. Polygon terms we know: Polygons Descriptors or parts Quadrilateral Pentagon Concave Trapezoid Convex Hexagon Kite Octogon Rectangle Vertex Side Square Diagonal Regular Polygon

  3. 6-1The Polygon Angle-Sum Theorems Objective: To find the sum of the measures of the interior angles of a polygon To find the sum of the measures of the exterior angles of a polygon

  4. Polygon Sum Theorem Theorem 6-1 The sum of the measures of the n interior angles of an n-gon is ______________. 1800 (n – 2) Example: Rectangle – 4 interior angles 4 right angles 4 (900) = 3600 The sum of the measures of the interior angles of a quadrilateral is 3600 nth term: 1800 (n – 2) n = 4 1800 (4 -2)= 3600

  5. Three Types of Polygons

  6. a + b + c = 1800 x + y + z = 1800 x a Triangle Sum Conjecture y (a + b + c) + (x + y + z) = 3600 b Addition Property of equality Sum of the measures of the interior angles of a quadrilateral equals 3600 c z

  7. p. 356: 7, 9, 11, 15, 17, 19, 21, 23, 25, 29, 31

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