Unit 3 Comp 4 Interior/Exterior Angles of a Polygon

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Presentation transcript:

Unit 3 Comp 4 Interior/Exterior Angles of a Polygon R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon interior and exterior angle measure of a regular polygon or irregular polygon number of sides or angles of a polygon

Definitions Interior Angle: The inside angle of a polygon formed by two adjacent sides Exterior Angle: The angle formed when one side of a polygon is extended (adjacent to an interior angle) Remote Interior Angles: In a triangle, the two angles that are not adjacent to a specific exterior angle

Exterior Angles Lab Name the interior angles: _______ _______ C D Name the interior angles: _______ _______ Name the exterior angle shown:_______ Which interior angles are remote interior angles?

Part 1: Measure each angle with your protractor and record your results in the chart. . . B C D +

Part 1 (continued): X W Y Z +

Conjecture: The measure of an exterior angle of a triangle is equal to: The sum of the interior angles of a triangle is always: The sum of the remote interior angles! 180 degrees!

Examples Find the value of the variable for each triangle. Classify each triangle by its angles. 120o y x 40o 60o x

You Try… 180-84-27 = x X = 69o 180-90-65 = z Z = 25o Y = 84 + 27

You Try… 2x+5 + x-25 + 2x = 180 5x – 20 = 180 5x = 200 X = 40 (2x + 5)o (x - 25)o 2xo 2x+5 + x-25 + 2x = 180 5x – 20 = 180 5x = 200 X = 40 78 + y = 110 Y = 32o 78+32+x = 180 X = 70o

Polygons Polygon: A geometric figure formed by line segments that meet at their endpoints, do not cross, and completely enclose part of a plane.

Draw Examples of . . . Polygons Not Polygons

Definitions Convex Polygon: A polygon in which no segment connecting two vertices is outside the polygon Examples:

Definitions Concave Polygon: A polygon in which at least one segment connecting two vertices is outside the polygon. Examples:

Definitions Consecutive Sides: Consecutive Vertices: Consecutive Angles: Two sides that share a common vertex Two vertices connected by a side Two angles that share a common side

Classifying Polygons According to Numbers of Sides Number of Sides Name of Polygon 1 2 3 4 5 6 Not a polygon Not a polygon Triangle Quadrilateral Pentagon Hexagon

Classifying Polygons According to Numbers of Sides Number of Sides Name of Polygon 7 8 9 10 11 12 n Heptagon Octagon Nonagon Decagon Hendecagon Dodecagon N-gon