Geom 6point1 97
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Geom 6point1 97 Presentation Transcript

  • 1. 6.1 Quadrilaterals Objectives: - Identify, name, and describe polygons - Use the sum of the measures of the interior angles of a quadrilateral.
  • 2. Polygons
    • A polygon is a plane figure that
      • Is formed by 3 or more segments called sides, such that no 2 sides with a common endpoint are collinear.
      • each side intersects exactly two other sides, one at each endpoint
  • 3. Polygons
    • Each endpoint of a side is a vertex of the polygon.
    • You can name the polygon by listing its vertices consecutively.
  • 4. Identifying Polygons
    • Which of these shapes is a polygon?
  • 5. Polygon are named by the number of sides they have. 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n -gon
  • 6. Convex/Concave
    • A polygon is convex if no line that contain a side of the polygon contains a point in the interior of the polygon.
    • A polygon that is not convex is called nonconvex or concave .
  • 7. Convex/Concave
    • A polygon is equilateral if all its sides are congruent.
    • A polygon is equiangular if all its internal angles are congruent.
    • A polygon is regular if it is equilateral and equiangular.
  • 8. Interior Angles of Quadrilaterals
    • A diagonal of a polygon is a segment that joins two nonconsecutive vertices.
    • Like triangles, quadrilaterals have both interior and exterior angles. If you divide it into 2 triangles, each triangle has interior angles with measures that add up to . . .
    • 180
    • So, the sum of measures of the interior angles of a quadrilateral is 2*180˚ = 360˚
  • 9. Interior Angles of a Quadrilateral Theorem
    • The sum of the measures of the interior angles of a quadrilateral is 360˚.
  • 10. Example . . .
    • What is x?
    • 4x + 3x + 50 + 30 =
    • 360
    • 7x + 80 = 360
    • 7x = 280
    • x = 40
    50˚ 4x 3x 30˚
  • 11. Do p. 325 1-11, 48-51
    • Homework: Worksheets