CHAPTER 3: PARALLEL LINES AND PLANES Section 3-5: Angles of Polygons

POLYGONS Polygons are formed by coplanar segments (sides) where: 1.Each segment (side) intersects exactly two other segments, one at each endpoint. 2.No two segments (sides) with a common endpoint are collinear.

POLYGONS PolygonsNot Polygons

CLASSIFYING POLYGONS Polygons are classified according to the number of sides they have. 3 sidestriangle 4 sidesquadrilateral 5 sidespentagon 6 sideshexagon 8 sidesoctagon 10 sidesdecagon

POLYGON VOCABULARY We refer to polygons by listing its vertices in consecutive order. A diagonal of a polygon is a segment that joins two nonconsecutive vertices. We can find the sum of the measures of the interior angles of a polygon by drawing all diagonals from one vertex.

POLYGON 1.What type of polygon is shown? A hexagon 2.Name the polygon. Hexagon ABCDEF 3.Draw the diagonals of the polygon. AB C D F E

POLYGON MEASURES Since we know that the sum of the measures of the interior angles of a triangle is 180, we can find the measure of polygons by determining how many triangles it contains.

Consider the following polygons: TriangleQuadrilateralPentagon Hexagon 3 sides4 sides5 sides 6 sides 1 triangle2 triangles3 triangles 4 triangles 180(1)=180(2)=180(3)= 180(4)=

THEOREMS Theorem 3-13: The sum of the measures of the interior angles of a convex polygon with n sides is (n – 2)180. Theorem 3-14: The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.

POLYGON SPECIFICS Polygons can be: Equiangular Equilateral Both equiangular and equilateral (Regular Polygons).

REGULAR POLYGONS Take the following scenarios into account: Not equiangularEquiangularEquilateral Regular nor equilateral 120

CLASSWORK/HOMEWORK Pg. 103, Classroom Exercises 1-9 Pg. 104, Written Exercises 2-20 even