Properties and Attributes of Polygons

1
6-1
Properties and Attributes of Polygons
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
2
Warm Up 1. A ? is a three-sided
polygon. 2. A ? is a four-sided
polygon. Evaluate each expression for n 6. 3.
(n 4) 12 4. (n 3) 90 Solve for a. 5. 12a
4a 9a 100
triangle
quadrilateral
24
270
4
3
Objectives
Classify polygons based on their sides and
angles. Find and use the measures of interior
and exterior angles of polygons.
4
Vocabulary
side of a polygon vertex of a polygon diagonal reg
ular polygon concave convex
5
Each segment that forms a polygon is a side of
the polygon. The common endpoint of two sides is
a vertex of the polygon. A segment that connects
any two nonconsecutive vertices is a diagonal.
6
You can name a polygon by the number of its
sides. The table shows the names of some common
polygons.
7
(No Transcript)
8
Example 1A Identifying Polygons
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of sides.
polygon, hexagon
9
Example 1B Identifying Polygons
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of sides.
polygon, heptagon
10
Example 1C Identifying Polygons
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of sides.
not a polygon
11
Check It Out! Example 1a
Tell whether each figure is a polygon. If it is a
polygon, name it by the number of its sides.
not a polygon
12
Check It Out! Example 1b
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of its sides.
polygon, nonagon
13
Check It Out! Example 1c
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of its sides.
not a polygon
14
All the sides are congruent in an equilateral
polygon. All the angles are congruent in an
equiangular polygon. A regular polygon is one
that is both equilateral and equiangular. If a
polygon is not regular, it is called irregular.
15
A polygon is concave if any part of a diagonal
contains points in the exterior of the polygon.
If no diagonal contains points in the exterior,
then the polygon is convex. A regular polygon is
always convex.
16
Example 2A Classifying Polygons
Tell whether the polygon is regular or irregular.
Tell whether it is concave or convex.
irregular, convex
17
Example 2B Classifying Polygons
Tell whether the polygon is regular or irregular.
Tell whether it is concave or convex.
irregular, concave
18
Example 2C Classifying Polygons
Tell whether the polygon is regular or irregular.
Tell whether it is concave or convex.
regular, convex
19
Check It Out! Example 2a
Tell whether the polygon is regular or irregular.
Tell whether it is concave or convex.
regular, convex