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Unit 24

Unit 24. POLYGONS. TYPES OF POLYGONS. A polygon is a closed plane figure formed by three or more straight line segments A convex polygon is a polygon in which no side, if extended, cuts inside the polygon

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Unit 24

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  1. Unit 24 POLYGONS

  2. TYPES OF POLYGONS • A polygon is a closed plane figure formed by three or more straight line segments • A convex polygon is a polygon in which no side, if extended, cuts inside the polygon • A concave polygon is a polygon in which two or more sides, if extended, cut inside the polygon

  3. TYPES OF POLYGONS • An equilateral polygon is a polygon with all sides equal • An equiangular polygon is a polygon with all angles equal • A regular polygon is a polygon that is both equilateral and equiangular; all sides and all angles are equal • A quadrilateral is a polygon with four sides

  4. TYPES OF QUADRILATERALS • A trapezoid is a quadrilateral that has only two sides parallel • A parallelogram is a quadrilateral whose opposite sides are parallel and equal • A rectangle is a special type of parallelogram whose angles each equal 90°

  5. TYPES OF QUADRILATERALS • A square is a special type of rectangle whose sides are all equal • A rhombus is a special type of parallelogram whose sides are all equal, but whose angles are not all equal • A pentagon is a polygon with five sides • A hexagon is a polygon with six sides • An octagon is a polygon with eight sides

  6. INTERIOR ANGLES OF A POLYGON • The sum of the interior angles of a polygon of n sides is equal to (n – 2) × 180° • Find the sum of the interior angles of the figure shown below: • The figure has six sides, so it is a hexagon • Since there are six sides, the sum of the interior angles would be: (6 – 2)  180 = 4  180 = 720 Ans

  7. EXTERIOR ANGLES • If a side of a polygon is extended, the angle between the extended side and the adjacent side of the polygon is an exterior angle • The sum of the exterior angles of any polygon, formed as each side is extended in succession, is equal to 360

  8. EXTERIOR ANGLES EXAMPLE • Find the number of sides of a regular polygon having an exterior angle of 24° • Since the sum of the exterior angles of any polygon is 360°, divide 360° by 24° • 360°  24° = 15 sides Ans

  9. A B E F C D MEDIAN OF A TRAPEZOID • A median of a trapezoid is a line that joins the midpoints of the nonparallel sides (legs) • The median of a trapezoid is parallel to the bases and equal to one half the sum of the bases Line EF is the median

  10. A B E F C D MEDIAN OF A TRAPEZOID EXAMPLE • Find the length of EF in the trapezoid shown below given that AB || CD, EF is the median, AB = 40 m, and CD = 26 m • Since EF is the median, it is equal to one half the sum of the bases (AB plus CD) • EF = 1/2(40 m + 26 m) = 33 m Ans

  11. PRACTICE PROBLEMS • Define each of the following. • Concave polygon • Regular polygon • Quadrilateral • Are all quadrilaterals parallelograms? Explain. • Are all squares rectangles? Explain.

  12. 6. 7. 8. 9. PRACTICE PROBLEMS (Cont) • Identify each of the polygons below using at least one of the definitions given in this unit.

  13. PRACTICE PROBLEMS (Cont) • Find the number of degrees in the sum of the interior angles of each of the following figures. a. pentagon b. 7-sided polygon c. 9-sided polygon • Find the number of degrees in each exterior angle of the regular figures given below. a. octagon b. 10-sided polygon c. 9-sided polygon

  14. 72° 70° 115° 1 PRACTICE PROBLEMS (Cont) • Find the number of degrees in 1 in the polygon shown below.

  15. 312 in C E 156 in A 136 in 120 in B F D 166 in 332 in PRACTICE PROBLEMS (Cont) • Determine length CD in the figure at right given that CD || AB.

  16. PROBLEM ANSWER KEY • A polygon in which two or more sides, if extended, cut inside the polygon • A polygon that is both equilateral and equiangular; all sides and all angles are equal • A polygon with four sides • No, a parallelogram is a quadrilateral whose opposite sides are parallel and equal. Not all quadrilaterals have parallel and equal opposite sides • Yes, squares are a special type of rectangle whose sides are all equal

  17. PROBLEM ANSWER KEY (Cont) • Regular pentagon • Trapezoid • Hexagon • Parallelogram or quadrilateral • a. 540° b. 900° c. 1260° • a. 45° b. 36° c. 40° • 103° • 152 inches

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