 # NAMING POLYGONS.

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NAMING POLYGONS

What does the word “polygon” mean?
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

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

Polygons can be CONCAVE or CONVEX

Ex. 3 Classify each polygon as convex or concave.

Diagonals & Angle Measures

What is the sum of the measures of the interior angles of a triangle?
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 Sum of measures of interior angles # 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°

Two more important terms
Interior Angles Exterior Angles

1 2 3 4 5 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
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 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 # even Page 411 # 8-18 all

Foldable for Formulas Sum of INTERIOR Angles ONE INTERIOR Angle Sum
EXTERIOR Angles ONE EXTERIOR Angle