Chapter 8: Quadrialterals

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Presentation transcript:

Chapter 8: Quadrialterals Section 8.1: Find Angle Measures in Polygons

Section 8.1: Find Angle Measures in Polygons Polygon: Literally means “many angles/sides” A figure made up of line segments called sides Must have at least 3 or more sides The figure must be closed No two sides may cross

Polygon Vertex (Vertices) B C Side CD Diagonal: a segment that joins two nonconsecutive vertices D A Polygon ABCD Take notice that the figure is closed & that the sides do not cross This is a convex polygon

Examples of Non-Polygons Not Closed Lines Cross Each Other

Section 8.1: Find Angle Measures in Polygons Convex Polygon: a polygon in which no line that contains a side of the polygon passes through the interior of the polygon “Normal Looking” Concave Polygon: A polygon that appears to cave in

Draw the following Polygons: Quadrilateral Triangle Pentagon Hexagon

Draw the following Polygons Heptagon Octagon Nonagon

Section 8.1: Find Angle Measures in Polygons Equilateral: A polygon in which all sides are congruent Equiangular: A polygon in which all angles are congruent Regular: A polygon that is both equilateral and equiangular

Section 8.1: Find Angle Measures in Polygons Polygon Interior Angle Theorem: The sum of the interior angles of a convex n-gon is: (n – 2)  180° Note: To find the measure of each angle in a regular polygon with n sides, use the following formula: Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360° Note: To find the measure of each exterior angle of a regular polygon with n sides, use the following formula:

Section 8.1: Find Angle Measures in Polygons The following polygons are equilateral. Find the perimeter 12 in 7 cm If this hexagon is equilateral and its perimeter is 39 in, how long is each side?

Section 8.1: Find Angle Measures in Polygons The polygons are regular. Find the value of x. 144° 60° (4x – 5)° (3x – 6)° 128.57° (4x + 3)°

Section 8.1: Find Angle Measures in Polygons Try together: Pg. 508 Guided Practice Problems #1- 5

Section 8.1: Find Angle Measures in Polygons Homework: Pg. 510 # 3-16 (all)