1. Chapter 6: Polygons and Quadrilaterals

2. Polygon terms we know: Kite Trapezoid Polygons Quadrilateral Rectangle Square Concave Convex Side Vertex Diagonal Regular Polygon Descriptors or parts Hexagon Pentagon Octogon

3. 6-1 The Polygon Angle-Sum Theorems Objective: To find the sum of the measures of the interior angles of a polygon To find the sum of the measures of the interior angles of a polygon To find the sum of the measures of the exterior angles of a polygon To find the sum of the measures of the exterior angles of a polygon

4. 1. Draw 2 of your assigned polygon. 2. Measure and label all interior angles. 3. Find the sum of all interior angles. 4. Compare your results with person sitting next to you. 1080 0 900 0 720 0 540 0 360 0 180 0 ?... Sum of interior angles n...876543 # of sides of polygon n th term: + 180 0 180 0 ( – 2) 180(3) + ______= 180 180(3) + 180(-2) = 180 180 (3 – 2) = 180 -360 n The sum of the measures of the n interior angles of an n- gon is ______________. Polygon Sum Conjecture 180 0 (n – 2)

5. Theorem 6-1 The sum of the measures of the n interior angles of an n-gon is ______________. Polygon Sum Theorem 180 0 (n – 2) n th term: 180 0 (n – 2) 180 0 (4 -2)= 360 0 Rectangle – 4 interior angles 4 right angles 4 (90 0 ) = 360 0 Example: n = 4 The sum of the measures of the interior angles of a quadrilateral is 360 0

6. Three Types of Polygons

7. Addition Property of equality Triangle Sum Conjecture x y zc b a a + b + c = 180 0 x + y + z = 180 0 (a + b + c) + (x + y + z) = 360 0

8. p. 356: 7, 9, 11, 15, 17, 19, 21, 23, 25, 29, 31