Transcript Using Patterns and Inductive Reasoning

Name the polygons with the
following number of sides:
•
•
•
•
•
•
•
•
•
3
4
5
6
7
8
9
10
12
•
•
•
•
•
•
•
•
•
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
Polygons
Geometry
Mrs. King
Unit 3, Lesson 4
Definition
Polygon: a closed plane
figure with at least
three sides.
Video: Polygons in Architecture
Name the polygon. Then identify its vertices, sides, and
angles.
Possible names are ABCDE and EDCBA.
Its vertices are A, B, C, D, and E.
Its sides are AB, BC, CD, DE, and EA.
Its angles are named by the vertices, A, B,
C, D, and E.
Without the use of your notes:
Matching names with number of sides:
http://www.quia.com/cm/86645.html?AP
_rand=2098901149
Concentration game:
http://www.quia.com/jg/1507267.html
Definition
Convex: a polygon is
convex if no diagonal
contains points
outside the polygon.
http://img.sparknotes.com/figures/B/b333d91dce2882b2db48b8ad670cd15a/convexconcave.gif
Definition
Concave: a polygon is
concave if a diagonal
contains points
outside the polygon.
http://img.sparknotes.com/figures/B/b333d91dce2882b2db48b8ad670cd15a/convexconcave.gif
Theorem 2-3: Polygon Interior
Angle-Sum Theorem
The sum of the
measures of the
interior angles of an
n-gon is (n - 2)180.
Find the sum of the measures of the angles of a decagon.
A decagon has 10 sides, so n = 10.
Sum = (n – 2)(180)
= (10 – 2)(180)
= 8 • 180
= 1440
Practice
• Find the sum of the measure of the interior angle
of the following polygons:
– 15-gon
– 20-gon
– Decagon
– Dodecagon
(n-2) x 180 video
• Cool Video!!
Find m  X in quadrilateral XYZW.
The figure has 4 sides, so n = 4.
Theorem 2-4: Polygon Exterior
Angle-Sum Theorem
The sum of the
measures of the
exterior angles of a
polygon, one at each
vertex, is 360.
http://www.mathlove.com/new3/product/img/TTA05/5.jpg
Video: General Definitions of
Polygons
Definition
Equilateral polygon: a
polygon with all sides
congruent.
Equiangular polygon: a
polygon with all angles
congruent.
Regular polygon: a polygon
that is both equilateral and
equiangular.