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Chapter 3 Polygons 3.1 Basic Polygons I. Properties of a Polygon A. A plane figure formed by three or more consecutive segments (sides or laterals) B. Each side intersects exactly two other sides at its endpoints. C. These intersections are called vertices. D. No three consecutive vertices are collinear. II. Types of Polygons 3 sides – triangle 4 sides – quadrilateral 5 sides – pentagon 6 sides – hexagon 7 sides – heptagon 8 sides – octagon 9 sides – nonagon 10 sides – decagon 12 sides – dodecagon 20 sides – icosagon n sides – n-gon III. Convex and Concave Polygons A. Convex – any two points inside of the polygon can be connected with a segment that is completely inside the polygon. B. Concave – opposite of convex IV. Regular Polygons A. Polygons that are both equilateral and equiangular. B. Equilateral – all the sides are the same length C. Equiangular – all the angles are the same measure. D. Perimeter – the distance around a polygon Regular Pentagon Diagonal – a segment connecting two non-consecutive vertices 3.2 Angles of Polygons I. Polygon Interior Angle Theorem 5 sides -- pentagon 3 triangles x 180 540° 3.2 Angles of Polygons I. Polygon Interior Angle Theorem 6 sides -- hexagon 4 triangles x 180 720° Total number of degrees in a polygon = 180(n – 2) 3.2 Angles of Polygons I. Polygon Interior Angle Theorem 6 sides -- hexagon 110° x + 30 4 triangles x 180 95° 720° 122° 103° x II. Regular Polygons 180 (n – 2) 180 (3) 540° 5 108° Each angle of a regular polygon = 180(n – 2) n Regular Octagon 180 ( n – 2) 180 ( 6) 1080° 8 135° III. Polygon Exterior Angle Theorem 72° 108° 72° 108° 108° 72° 108° 108° 72° 72° The sum of the measures of the exterior angles of a polygon is 360° 3.3 Types of Quadrilaterals I. Parallelogram - quadrilateral with opposite sides that are parallel and congruent 55° 125° 55° 125° Opposite angles are equal in measure II. Rectangle A parallelogram with four right angles. III. Rhombus Parallelogram with four congruent sides 120° 60° 60° 120° IV. Square Parallelogram with four congruent sides and four right angles A square is a parallelogram, a rectangle, and a rhombus. V. Trapezoid A quadrilateral with one pair of parallel sides 3.4 Trapezoids Parallel sides are called the bases. Non-parallel sides are called the legs. I. Special Trapezoids A. Isosceles Trapezoid a trapezoid with two congruent sides 110° 70° Base angles are congruent 110° 70° I. Special Trapezoids B. Right Trapezoid a trapezoid with two right angles 125° 55° II. Trapezoid Midsegment Theorem A 25 cm. MS = (sum of bases)2 B MS = (25 + 39)2 E C 32 cm. 39 cm. MS = (64)2 MS = 32 F D