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Chapter 6 Definitions

"The main difference between a cat and a lie is that a cat only has nine lives." Mark Twain. Chapter 6 Definitions. Parallelogram Rectangle Rhombus Square Trapezoid Diagonal Base Legs. Interior Angles of Polygons. 180 . 180 . 180 . 180 . 180 . 180 + 180 = 360  .

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Chapter 6 Definitions

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  1. "The main difference between a cat and a lie is that a cat only has nine lives." Mark Twain Chapter 6 Definitions • Parallelogram • Rectangle • Rhombus • Square • Trapezoid • Diagonal • Base • Legs

  2. Interior Angles of Polygons 180 180 180 180 180 180+ 180= 360 180+ 180 + 180 = 540 180 180 180 180 180+180+ 180 + 180 + 180 = 900 180+ 180 + 180 + 180 = 720

  3. Interior Angles Sum Theoreom If a convex polygon has n sides and S is the sum of the measures of its interior angles then S=180(n-2)

  4. Application – Regular Polygon • The benzene molecule C6H6 consists of six carbon atoms in a regular hexagonal pattern with a hydrogen atom attached to each carbon atom. Find the sum of the measures of the interior angles of the hexagon. • Convex Polygon • S=180(n-2) • S=180(6-2) • S=180(4) • S=720

  5. Application – Regular Polygon • A mall is designed so the five walkways meet at a food court that is in the shape of a regular pentagon. Find the sum of the measures of the interior angles of the pentagon. • Convex Polygon • S=180(n-2) • S=180(5-2) • S=180(3) • S=540

  6. Irregular Polygon C B • Find the measures of the angles. • 360=mA + mB +mC + mD • 360 = x + 2x +2x + x • 360 = 6x • x = 60 • mA & mD = 60, mB & mC = 180 2x 2x x x A D

  7. Exterior Angle Sum Theorem 2 If a polygon is convex, then the sum of the measure of the exterior angles, one at each vertex is 360 1 2 6 3 7 5 4 8 4 1 3 1 3 2

  8. Exterior Angles • Find the measures of an exterior angle and an interior angle of the convex regular octagon ABCDEFGH • Interior Angles • S=180(n-2) • S=180(6) • S=1080 • Individual Interior Angles • S=1080/8 • = 135 • Exterior Angles • 360/8 = 45 • Note Exterior & Interior Angle are a Linear Pair (supplementary) 135+45 = 180

  9. Summary • For Convex Polygons • Measure of Interior Angles = 180(n-2) • Measure of Exterior Angles = 360 Practice Assignment Block Page 394 12 - 32 even

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