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## NAMING POLYGONS

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**NAMING**POLYGONS**Let's Discuss**What does the word “polygon” mean? What is the smallest number of sides a polygon can have? What is the largest number of sides a polygon can have?**Triangle**Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon Hexagon n-gon Heptagon**Hip Bone’s connected to the…Classifying Polygons**Polygons with 3 sides… Triangles Polygons with 4 sides… Quadrilaterals Polygons with 5 sides.. Pentagons But wait we have more polygons Polygons with 6 sides… Hexagons Polygons with 7 sides… Heptagons Polygons with 8 sides… Octagons But still we have more polygons Polygons with 9 sides… Nonagons Polygons with 10 sides… Decagons Polygons with 12 sides… Dodecagons And now we have our polygons**A VERTEX is the point of intersection of two sides**CONSECUTIVE VERTICESare two endpoints of any side. A B F C A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL. E D Sides that share a vertex are called CONSECUTIVE SIDES. Important Terms**More Important Terms**EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruent REGULAR- All sides and angles are congruent**Polygons are named by listing its vertices consecutively.**A B C F E D**Polygons can be CONCAVE or CONVEX**CONCAVE CONVEX**Ex. 3 Classify each polygon as convex or concave.**Concave Concave Concave CONVEX**Diagonals &**Angle Measures**REVIEW:**What is the sum of the measures of the interior angles of a triangle? 180° 180° 180° What is the sum of the measures of the interior angles of any quadrilateral? 360°**Sum of measures of interior angles**# of triangles # of sides 1(180) = 180 3 1 2(180) = 360 4 2 3 3(180) = 540 5 6 4 4(180) = 720 n-2 (n-2) 180 n**If a convex polygon has n sides, then the sum of the measure**of the interior angles is (n – 2)(180°)**Ex. 1 Use the regular pentagon to answer the questions.**• Find the sum of the measures of the interior angles. • Find the measure of ONE interior angle 540° 108°**Interior Angles**Exterior Angles Two more important terms**2**1 3 5 4 If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.**If any convex polygon, the sum of the measures of the**exterior angles, one at each vertex, is 360°. 1 3 2**If any convex polygon, the sum of the measures of the**exterior angles, one at each vertex, is 360°. 1 2 4 3**Ex. 2 Find the measure of ONE exterior angle of a regular**hexagon. 60°**Ex. 3 Find the measure of ONE exterior angle of a regular**heptagon. 51.4°**Ex. 4 Each exterior angle of a polygon is 18. How many**sides does it have? n = 20**Ex. 5 The sum of the measures of five interior angles of a**hexagon is 535. What is the measure of the sixth angle? 185°**Ex. 6 The measure of the exterior angle of a quadrilateral**are x, 3x, 5x, and 3x. Find the measure of each angle. 30°, 90°, 150°, and 90°**Ex. 7 If each interior angle of a regular polygon is 150,**then how many sides does the polygon have? n = 12**Practice Time**Practice Worksheet 10-2**Homework:**Page 406 # 16-32 even Page 411 # 8-18 all