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# Geom 6point1 97

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### Geom 6point1 97

1. 1. 6.1 Quadrilaterals Objectives: - Identify, name, and describe polygons - Use the sum of the measures of the interior angles of a quadrilateral.
2. 2. Polygons <ul><li>A polygon is a plane figure that </li></ul><ul><ul><li>Is formed by 3 or more segments called sides, such that no 2 sides with a common endpoint are collinear. </li></ul></ul><ul><ul><li>each side intersects exactly two other sides, one at each endpoint </li></ul></ul>
3. 3. Polygons <ul><li>Each endpoint of a side is a vertex of the polygon. </li></ul><ul><li>You can name the polygon by listing its vertices consecutively. </li></ul>
4. 4. Identifying Polygons <ul><li>Which of these shapes is a polygon? </li></ul>
5. 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. 6. Convex/Concave <ul><li>A polygon is convex if no line that contain a side of the polygon contains a point in the interior of the polygon. </li></ul><ul><li>A polygon that is not convex is called nonconvex or concave . </li></ul>
7. 7. Convex/Concave <ul><li>A polygon is equilateral if all its sides are congruent. </li></ul><ul><li>A polygon is equiangular if all its internal angles are congruent. </li></ul><ul><li>A polygon is regular if it is equilateral and equiangular. </li></ul>
8. 8. Interior Angles of Quadrilaterals <ul><li>A diagonal of a polygon is a segment that joins two nonconsecutive vertices. </li></ul><ul><li>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 . . . </li></ul><ul><li>180 </li></ul><ul><li>So, the sum of measures of the interior angles of a quadrilateral is 2*180˚ = 360˚ </li></ul>
9. 9. Interior Angles of a Quadrilateral Theorem <ul><li>The sum of the measures of the interior angles of a quadrilateral is 360˚. </li></ul>
10. 10. Example . . . <ul><li>What is x? </li></ul><ul><li>4x + 3x + 50 + 30 = </li></ul><ul><li>360 </li></ul><ul><li>7x + 80 = 360 </li></ul><ul><li>7x = 280 </li></ul><ul><li>x = 40 </li></ul>50˚ 4x 3x 30˚
11. 11. Do p. 325 1-11, 48-51 <ul><li>Homework: Worksheets </li></ul>