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Notes: 6-1 Angles of Polygons Diagonal – Polygon # of Sides # of Triangles Sum of Interior Angle Measures Triangle Quadrilateral Pentagon Hexagon n-gon How do you calculate the sum of the interior angles of a polygon? Theorem 6.1 – Polygon Interior Angles Sum Review: Naming Polygons # of Sides Polygon 3 4 5 6 7 8 # of Sides 9 10 11 12 n Polygon Example 1: a. Find the sum of the measures of the interior angles of a convex heptagon. Measure the heptagon below with a protractor to see if your sum is correct. b. Find the measure of each interior angle of quadrilateral ABCD. Example 2: The poles for a tent form the vertices of a regular hexagon. When the poles are properly positioned, what is the measure of the angle formed at a corner of the tent? Polygon Exterior Angle Sum What do you notice about the exterior angles of a polygon? Notes: 6-2 Parallelograms Parallelogram – Example 1: In parallelogram ABCD, suppose m<A = 55, AB = 2.5 feet, and BC = 1 foot. Find each measure. a. DC = b. m<B = c. m<C = Example 2: If QRST is a parallelogram, find the value of the indicated variable. a. x b. y c. z Geogebra Activity: Draw parallelogram ABCD with vertices at A(5,1), B( 2, 1), C(4,5), D(7,5). Cut and paste your parallelogram here: A. Use the Midpoint Formula to determine if the diagonals of ABCD bisect each other. B. Determine whether the diagonals are congruent. C. Use slopes to determine if the consecutive sides are perpendicular. Explain.