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Transcript
Name: _____________________________ Geometry Ch. 6.1: Angles of Polygons We will now be moving from studying the properties of triangles to studying the properties of quadrilaterals. Polygon: A ________ figure formed by a finite number of coplanar _____________ called sides such that: The sides that have a common endpoint are _________________ Each side intersects exactly ________ other sides but only at the _____________ Diagonal of a Polygon: A segment that connects any two nonconsecutive vertices Find an expression for the sum of the angles of an n-sided convex polygon. Number of sides (n) Sum of interior angles (s) Theorem 6.1: The sum of the interior angle measures of an n-sided convex polygon is ___________________ Example: What is the sum of the angle measures of a 27-gon? Name: _____________________________ Geometry Ch. 6.1: Angles of Polygons Now we are going to look at the exterior angles of a polygon and see if we can develop a theorem like we did for interior angles. To draw the exterior angles, you have to keep your orientation consistent. Start at one vertex and move either clockwise or counter-clockwise, extending each side as you move along. Use algebra with a triangle, quadrilateral, pentagon, and hexagon to determine the sum of the exterior angles of those polygons. Begin by labeling the interior angles with arbitrary letters. Try to think of how you would justify your hypothesis for any n-gon since we cannot draw all possible cases. The proof will be in your homework. Theorem 6.2 – Polygon Exterior Angles Sum: The sum of the exterior angle measures of a convex polygon, one angle at each vertex, is _________ degrees.