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Chapter 3

Chapter 3. Polygons. 3.1 Basic Polygons. I. Properties of a Polygon. A plane figure formed by three or more consecutive segments (sides or laterals) Each side intersects exactly two other sides at its endpoints. These intersections are called vertices.

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Chapter 3

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  1. Chapter 3 Polygons

  2. 3.1 Basic Polygons I. Properties of a Polygon • A plane figure formed by three or more consecutive segments (sides or laterals) • Each side intersects exactly two other sides at its endpoints. • These intersections are called vertices. • No three consecutive vertices are collinear.

  3. 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

  4. III. Convex and Concave Polygons • Convex – any two points inside of the polygon can be connected with a segment that is completely inside the polygon. • Concave – opposite of convex

  5. IV. Regular Polygons • Polygons that are both equilateral and equiangular. • Equilateral – all the sides are the same length • Equiangular – all the angles are the same measure. • Perimeter – the distance around a polygon

  6. Regular Pentagon

  7. Diagonal – a segment connecting two non-consecutive vertices

  8. 3.2 Angles of Polygons I. Polygon Interior Angle Theorem 5 sides -- pentagon 3 triangles x 180 540°

  9. 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)

  10. 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

  11. II. Regular Polygons 180 (n – 2) 180 (3)  5 540° 108° Each angle of a regular polygon = 180(n – 2)  n

  12. Regular Octagon 180 ( n – 2) 180 ( 6) 1080° 8 135°

  13. III. Polygon Exterior Angle Theorem 72° 108° 72° 108° 108° 72° 72° 108° 108° 72° The sum of the measures of the exterior angles of a polygon is 360°

  14. 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

  15. II. Rectangle A parallelogram with four right angles.

  16. III. Rhombus Parallelogram with four congruent sides 120° 60° 60° 120°

  17. IV. Square Parallelogram with four congruent sides and four right angles A square is a parallelogram, a rectangle, and a rhombus.

  18. V. Trapezoid A quadrilateral with one pair of parallel sides

  19. 3.4 Trapezoids Parallel sides are called the bases. Non-parallel sides are called the legs.

  20. I. Special Trapezoids A. Isosceles Trapezoid a trapezoid with two congruent sides 110° 110° 70° 70° Base angles are congruent

  21. I. Special Trapezoids B. Right Trapezoid a trapezoid with two right angles 125° 55°

  22. II. Trapezoid Midsegment Theorem MS = (sum of bases)2 A 25 cm. B MS = (25 + 39)2 MS = (64)2 MS = 32 32 cm. E F C D 39 cm.

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