2. Simplify the expression 6y-(2y-1)-4(3y+2) a. -8y-7b. -8y-3 c. -8y+1d. -8y+7 2 1.8 warm-up 2

3. Pardekooper

4. Lets start with some common terms. Polygon –A–A–A–A closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear.

5. Yes No, it has no sides No, it is not a plane figure No, two sides Intersect Between endpoints

6. Lets start with some common terms. Regular Polygon –A–A–A–All the sides are congruent –A–A–A–All the angles are congruent Pardekooper

7. Name all the polygons below A B C D E polygon ABCDE polygon ABE polygon BCDE

8. Now name the parts of the polygon A B C D E Vertices: A, B, C, D, E, Sides: AB, BC, CD, DE, EA Angles:  A,  B,  C,  D,  E

9. Lets name the polygons

10. 7 heptagon 11 hendecagon 5 pentagon 6 hexagon # of sides name 3 triangle 4 quadrilateral 8 octagon 9 nonagon 10 decagon 12 dodecagon n n-gon

11. How about different types of polygons Convex polygons no diagonal with points outside the polygon

12. How about different types of polygons Concave polygons at least one diagonal with points outside the polygon Pardekooper

13. Just two more theorems ! Polygon Angle-Sum Theorem Pardekooper The sum of the measures of the interior angles of a n-gon is (n-2)180. Example: Find the sum of the measures of the angles of a 15-gon. n = 15 formula: (n-2)180 (15-2)180 (13)180 2340

14. Pardekooper 117 0 100 0 x 0 115 0 105 0 How many sides ? 5 sides Use the formula to find out how many degrees. (n-2)180 (5-2)180 (3)180 540

15. Just one more theorem ! Polygon Exterior Angle-Sum Theorem Pardekooper The sum of the measures of the exterior angles of a polygon, one at each vertex is 360. 1 2 3 4 5 6 m  1 + m  2 + m  3 + m  4 + m  5 + m  6 = 360