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1.8 warm-up 2

1.8 warm-up 2. Simplify the expression 6y-(2y-1)-4(3y+2) a. -8y-7 b. -8y-3 c. -8y+1 d. -8y+7. 2. Polygon Angle-Sum Theorems. Pardekooper. Lets start with some common terms. Polygon

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1.8 warm-up 2

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

  2. Polygon Angle-Sum Theorems Pardekooper

  3. Lets start with some common terms. • Polygon • 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. Pardekooper

  4. Yes Are the following polygons ? No, two sides Intersect Between endpoints No, it is not a plane figure No, it has no sides Pardekooper

  5. Lets start with some common terms. • Regular Polygon • All the sides are congruent • All the angles are congruent Pardekooper

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

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

  8. Lets name the polygons

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

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

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

  12. Just two more theorems ! Polygon Angle-Sum Theorem 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-2)180 formula: n = 15 (15-2)180 (13)180 2340 Pardekooper

  13. Find the missing angle. Use the formula to find out how many degrees. (n-2)180 How many sides ? (5-2)180 1170 1000 (3)180 x0 540 1050 1150 5 sides Pardekooper

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

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