Geom 6point1 97
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This document provides objectives and information about polygons and quadrilaterals. It defines polygons and their properties such as sides, vertices, and types. It specifically discusses quadrilaterals, stating that if a quadrilateral is divided into two triangles, the sum of the interior angles is 180 degrees for each triangle, so the total sum of interior angles in a quadrilateral is 2 * 180 = 360 degrees. An example problem demonstrates using this property to find the measure of an unknown angle.
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Geom 6point1 97
- 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