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Transcript
Bell Work • Summarize your mistakes into five main things you did wrong or topics you did not understand during the Chapter 7 Test. List them. • What are three things you could have done differently to study for the Chapter 7 Test. • Set a goal for Chapter 8. Introduction to Chapter 8 • An n-gon is a polygon with n sides and n vertices. • Use a straightedge to draw convex polygons with the following number of sides • • • • 3 4 5 6 • In each polygon draw all the diagonals from one vertex. • A diagonal is a segment that joins two nonconsecutive vertices. Introduction to Chapter 8 Polygon Triangle Quadrilateral Pentagon Hexagon Number of Sides 3 Number of Triangles 1 Sum of Measures of Interior Angles 180° Introduction to Chapter 8 • Look for a pattern in the last column of your table. • What would the sum of measures of the interior angles of a convex heptagon be? Convex octagon? • Write a rule for the sum of the measures of the interior angles in a convex n-gon. • Would the sum of the interior angles change if we changed the side lengths? Warm-Up Exercises Notes Theorems Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n – 2)180° Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is ______. Warm-Up1Exercises EXAMPLE Find the sum of angle measures in a polygon Find the sum of the measures of the interior angles of a convex octagon. Warm-Up2Exercises EXAMPLE Find the number of sides of a polygon The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the number of sides. Warm-Up Exercises GUIDED PRACTICE 1. The coin shown is in the shape of a regular 11- gon. Find the sum of the measures of the interior angles. 2. The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon by the number of sides. Warm-Up3Exercises EXAMPLE Find an unknown interior angle measure ALGEBRA Find the value of x in the diagram shown. Warm-Up Exercises GUIDED PRACTICE 3. Use the diagram at the right. Find m S and m T. 4. The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle. Warm-Up Exercises Notes Theorems Polygon Exterior Angles Theorem http://www.geogebratube.com/student/m123612 http://www.geogebratube.com/student/m144946 http://www.geogebratube.com/student/m36302 The sum of the measure of the exterior angles of a convex polygon, one angle at each vertex, is ______. Warm-Up4Exercises EXAMPLE Warm-Up Exercises GUIDED PRACTICE 5. A convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What is the measure of an exterior angle at the sixth vertex? Warm-Up5Exercises EXAMPLE The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle and (b) the measure of each exterior angle. Warm-Up Exercises Daily Homework Quick CheckQuiz 1. Find the sum of the measures of the interior angles of a convex 24-gon. 2. The sum of the measures of the interior angles of a convex polygon is 5040o. Classify the polygon by the number of sides. Warm-Up Exercises Daily Homework Quick CheckQuiz 3. Find the value of x. 4. Find the measures of an interior angle and an exterior angle of a regular 36-gon. Warm-Up Exercises For Tomorrow Homework HW: 8.1 (pg. 504-506) #1,4,8,12,17,24,25,28