What does the word polygon mean What is

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 Hexagon Dodecagon Heptagon n-gon

Hip Bone’s connected to the… Classifying 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

Important Terms A VERTEX is the point of intersection of two sides A B F A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL. CONSECUTIVE VERTICES are two endpoints of any side. C E D Sides that share a vertex are called CONSECUTIVE SIDES.

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.

REVIEW: What is the sum of the measures of the interior angles of a triangle? 180° What is the sum of the measures of the interior angles of any quadrilateral? 360°

# of sides # of triangles Sum of measures of interior angles 3 1 1(180) = 180 4 2 2(180) = 360 5 3 3(180) = 540 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. A)Find the sum of the measures of the interior angles. 540° B)Find the measure of ONE interior angle 108°

Two more important terms Interior Angles Exterior Angles

If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 2 1 3 5 4

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, 3 x, 5 x, and 3 x. 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