2. 6.1 Polygons Week 1 Day 2 January 7 th 2014

3. Warm UP: Identifying Polygons State whether the figure is a polygon. If it is not, explain why.

4. Essential Question : What is a polygon? How do we identify and classify polygons? How do we find angle measures of quadrilaterals?

5. Vocabulary Polygon Sides Vertex of a polygon Consecutive vertices Diagonal of a polygon

6. Definitions A polygon is a plane figure that is formed by three or more segments called sides. (a closed, sided figure) Each side intersects exactly two other sides at each of its endpoints. Each endpoint is a vertex of the polygon. Two vertices that are endpoints of the same side are consecutive vertices. A segment that joins two nonconsecutive vertices of a polygon is called a diagonal. Vertices side diagonal Consecutive vertices

7. Warm UP: Identifying Polygons State whether the figure is a polygon. If it is not, explain why. Not D – has a side that isn’t a segment – it’s an arc. Not E– because two of the sides intersect only one other side. Not F because some of its sides intersect more than two sides. Figures A, B, and C are polygons.

8. Polygons are named by the number of sides they have. Fill in the blank. Number of sidesType of polygon 3Triangle 4 5 6 7 8 Quadrilateral Pentagon Hexagon Heptagon Octagon

9. Quadrilateral Interior Angles Theorem The sum of the measures of the interior angles of a quadrilateral is 360°. A B C D m<A + m<B + m<C + m<D = 360°

10. Example Find m<Q and m<R. R x P S 2x° Q 80° 70° x + 2x + 70° + 80° = 360° 3x + 150 ° = 360 ° 3x = 210 ° x = 70 ° m< Q = x m< Q = 70 ° m<R = 2x m<R = 2(70°) m<R = 140 °

11. Homework Page 306 # 8-10, 16, 18