Geom 6point1 97
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    Geom 6point1 97 Geom 6point1 97 Presentation Transcript

    • 6.1 Quadrilaterals Objectives: - Identify, name, and describe polygons - Use the sum of the measures of the interior angles of a quadrilateral.
    • 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
    • Polygons
      • Each endpoint of a side is a vertex of the polygon.
      • You can name the polygon by listing its vertices consecutively.
    • Identifying Polygons
      • Which of these shapes is a polygon?
    • 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
    • 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 .
    • 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.
    • 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˚
    • Interior Angles of a Quadrilateral Theorem
      • The sum of the measures of the interior angles of a quadrilateral is 360˚.
    • Example . . .
      • What is x?
      • 4x + 3x + 50 + 30 =
      • 360
      • 7x + 80 = 360
      • 7x = 280
      • x = 40
      50˚ 4x 3x 30˚
    • Do p. 325 1-11, 48-51
      • Homework: Worksheets