Download Lesson 10-5

Lesson 11-5 Polygons
Polygon – a simple, closed figure formed by three or more line segments, called sides.
Regular Polygon – a polygon with all angles equal and all sides equal
Polygons are classified by the number of sides.
Number of sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
12
Dodecagon
20
Icosagon
Example 1 Classify Polygons
Determine whether the figure is a polygon. If it is,
classify the polygon. If it is not a polygon, explain
why.
The figure has 5 sides that only intersect at their endpoints.
It is a heptagon.
Diagonal – a line segment that joins two nonconsecutive vertices in a polygon.
Interior Angle – an angle formed at a vertex in a polygon.
Sum of the interior angles in a polygon with n-sides = (n-2)180⁰
Each interior angle of a regular polygon with n-sides = (n-2)180⁰
n
Standardized Test Example 2 Sum of Interior Angle Measures
Find the sum of the measures of the interior angles of an octagon.
A 720
C 1260
B 1080
D 1440
Read the Test Item
The sum of the measures of the interior angles is (n – 2)180. Since an octagon has 8
sides, n = 8.
Solve the Test Item
(n – 2)180 = (8 – 2)180
= 6(180) or 1080
Replace n with 8.
Simplify.
The sum of the measures of the interior angles of an octagon is 1080. The correct
answer is B.
All possible diagonals from one vertex of an octagon are
shown at the right. You can see that 6 triangles are formed. So B,
6  180 = 1080, is correct.
CHECK
Real-World Example 3 Measure of One Interior Angle
PLAYGROUND The playground at Hayes Elementary School is in the shape of a
regular pentagon. Find the measure of an interior angle of the playground.
Step 1
Find the sum of the measures of the interior angles of a pentagon.
A pentagon has 5 sides. So, n = 5.
(n – 2)180 = (5 – 2)180
= (3)180 or 540
Replace n with 5.
Simplify.
The measures of the interior angles is 540.
Step 2
Divide the sum of the measures by 5 to find the measure of one angle.
Since 540  5 = 108, the measure of an interior angle of the playground is 108.
Tessellation – a repetitive pattern of polygons that fit together with no overlaps or holes
Example 4 Find Tessellations
Determine whether or not a regular decagon can be used to make a tessellation. If
not, explain.
The measure of each angle in a regular decagon is 144°.
The sum of the measures of the angles where the vertices meet must be 360°. So,
solve 144n = 360.
144n = 360
144n 360
144 = 144
n = 2.5
Write the equation.
Divide each side by 144.
Simplify.
Since 144° does not divide evenly into 360°, a regular decagon cannot be used to
make a tessellation.