1. Chapter 6: Quadrilaterals Section 6.1: Polygons

2. polygon – a plane figure that meets the following conditions. 1)It is formed by three or more segments called SIDES, such that no two sides with a common endpoint are collinear. 2)Each side intersects exactly two other sides, one at each endpoint. vertex – each endpoint of a side of a polygon.

3. You can name a polygon by listing its vertices consecutively. Q R P S T PQRST and QPTSR are two names for the above polygon.

4. Polygons are named by the number of sides they have. 3 Triangle 4 Quadrilateral 5 Pentagon

5. 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon

6. 10 Decagon 11 Undecagon 12 Dodecagon

7. n n-gon A polygon is equilateral if all of its sides are congruent. A polygon is equiangular if all of its interior angles are congruent.

8. A polygon is regular if it is equilateral and equiangular.

9. convex – a polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. concave or nonconvex – a polygon that is not convex.

10. diagonal – a diagonal of a polygon is a segment that joins two nonconsecutive vertices.

11. Example 1: Decide whether the figure is a polygon. If it is not, explain why. a) yesb) no c) nod) yes

12. Example 2: Tell whether the polygon is best described as equiangular, equilateral, regular, or none. a) equiangular b) regular

13. c) equilateral d) none

14. HOMEWORK (Day 1) pg. 325 – 326; 4 – 9, 12 – 17, 18 – 20, 24 – 30 You are going to need a calculator for today’s lesson!

15. Theorem 6.1: Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360°. m 1 + m 2 + m 3 + m 4 = 360°.

16. Example 3: Use the information to find the measure of the missing angle. 113 + 82 + 51 = 246 360 – 246 = 114 The missing angle is 114°

17. Example 4: 82 + (25x – 2) + (25x + 1) + (20x – 1) = 360 70x + 80 = 360 -80 -80 70x = 280 70 70 x = 4

18. HOMEWORK (Day 2) pg. 325 – 327; 10 – 11, 31 – 34, 37 – 39, 41 – 44, 46