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6.1 Polygons
Objectives:
(1) The student will be able to identify, name, and
describe polygons.
(2) The student will be able to find the sum of the
measures of the interior angles of a
quadrilateral.
Toolbox:
Summary:
Polygon – is a plane figure that is formed
By 3 or more segments (sides) such that
No 2 sides with a common endpoint are
Collinear and each side intersects exactly
2 other sides one at each endpoint (vertex)
Naming Polygons – by their sides
Number of Sides Type of Polygon
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
12
Dodecagon
n
n-gon
Convex – if no line that contains a side of
the polygon contains a point in the interior
of the polygon (diagonal cannot be in the
exterior of the polygon)
Concave – a polygon that is not convex
Equilateral – all sides congruent
Equiangular – all angles congruent
Regular – if it is both equilateral & equiangular!
Diagonal – of a polygon is a segment that joins
2 nonconsecutive vertices
Interior Angles of a Quadrilateral
The sum of the measures of the interior angles
of a quadrilateral is 360°.
Examples:
~ See extra examples notes #1-3
4. Find m<F, m<G, and m<H.
5. Find m<K, m<L, & m<M. Is quadrilateral
JKLM regular?
Q: What is true of all points except the endpoints
on a diagonal of a convex polygon?
Q: What word describes a regular polygon by its
side lengths? By its angle measures?
Q: Describe how the sides of a polygon intersect.
Hmwk: #12-30(E) omit #22, 31-35, 37-47 omit #40
Something to think about: A polygon has at least a pair each
of supplementary angles and complementary angles. Can it
be a quadrilateral? Explain or give an example.