4
7.1 pgs. 359-366
EQ: How do we classify and name polygons? Date:
These are polygons: These are not polygons:
* Polygon: ___________________________________________________________________________ _____________________________________________________________________________
* Convex Polygon: * Concave Polygon *Regular Polygon Example 1: Naming and Classifying Polygons
Name the following polygon and identify its sides and angles.
Name: _____________
Sides: ___________________________
Angles: __________________________
Classify each polygon below by stating if it is convex, concave, or regular, and using the chart to identify it by the number of sides. a. b.
c. d.
e. f.
Sides
Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
12 Dodecagon
n n-gon
A T
N
C
R
Thy420
Ashape with straight closed sides thatonlyintersectat vertices
A 0 All anglesy are
andAll anglespoint Ifanyw vertexis mustbeout pointing in convex
ACNRTATEN TRT FALALCLN LR LT
Concave convexHexagon Pentagon
ConvexConcave
Quadrilateral Heptagon
Concave RegularDodecagon Octagon
11gonB gon
5
Investigation: Sum of Interior Angles of a Polygon Choose one vertex in each shape below. From that one vertex only, draw in as many diagonals as possible. Count the number of triangles in each shape and fill in the chart to find the sum of the degrees of an interior angle of any polygon.
Shape
Number of Sides
Number of Triangles
Number of Triangles x 180°
Sum of Degrees of Interior Angles
a. Explain how the number of sides of a polygon is related to the number of triangles it contains? _____________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________
b. Use inductive reasoning: What is the sum of the measures of the interior angles of a 30 sided polygon?
=
=
=
=
=
=
2 20
3 1 1 180 1800
2 4 2 2 180 360
3,2 5 3 3 180 5400
4as 6 4 4 180
7200,2347 5 5 1800 9000
5.234 8 6 6 1800 1080u
A convex polygon will always have 2 lesstriangles than the number of sides
30sides228 Triangles so 2861803 50400
