This document discusses classifying and identifying properties of polygons. It includes examples of identifying whether figures are polygons and if they are convex or concave. It also discusses classifying polygons by number of sides and identifying them as equilateral, equiangular or regular based on side and angle properties. Examples are provided of finding missing side lengths of regular polygons using equations. Students are asked to classify sample polygons, draw examples, and solve problems identifying polygon properties.

1. 1.61.6 Classify Polygons
Bell Thinger
1. Draw an acute angle and shade the interior.
2. Find the measure of the supplement of a
130º angle.
ANSWER
ANSWER 50
3. Find the measure of the complement of an
86 angle.
ANSWER 4

2. 1.6

3. 1.6Example 1
SOLUTION
Tell whether the figure is a polygon and whether it is
convex or concave.
Some segments intersect more than two segments,
so it is not a polygon.
a.
b. The figure is a convex polygon.
d. The figure is a concave polygon.
Part of the figure is not a segment, so it is not a
polygon.
c.
b. c.a. d.

4. 1.6

5. 1.6

6. 1.6Example 2
SOLUTION
Classify the polygon by the number of sides. Tell
whether the polygon is equilateral, equiangular, or
regular. Explain your reasoning.
a. b.
The polygon has 6 sides. It is equilateral and
equiangular, so it is a regular hexagon.
a.
The polygon has 4 sides, so it is a quadrilateral. It
is not equilateral or equiangular, so it is not
regular.
b.

7. 1.6Example 2
SOLUTION
Classify the polygon by the number of sides. Tell
whether the polygon is equilateral, equiangular, or
regular. Explain your reasoning.
c. The polygon has 12 sides, so it is a dodecagon.
The sides are congruent, so it is equilateral. The
polygon is not convex, so it is not regular.
c.

8. 1.6Guided Practice
Sketch an example of a convex heptagon and
an example of a concave heptagon.
1.
SAMPLE ANSWER

9. 1.6Guided Practice
Classify the polygon shown at
the right by the number of
sides. Explain how you know
that the sides of the polygon are
congruent and that the angles
of the polygon
are congruent.
2.
Quadrilateral. They all have the same measure;
they are all right angles.
ANSWER

10. 1.6Example 4
A table is shaped
like a regular hexagon.The
expressions shown represent
side lengths of the hexagonal
table. Find the length of a side.
ALGEBRA
SOLUTION
First, write and solve an equation to find the value of x.
Use the fact that the sides of a regular hexagon are
congruent.
Write equation.
Subtract 3x from each side.
Add 2 to each side.
3x + 6 4x – 2=
6 = x – 2
8 = x

11. 1.6Example 4
A table is shaped
like a regular hexagon.The
expressions shown represent
side lengths of the hexagonal
table. Find the length of a side.
ALGEBRA
SOLUTION
Then find a side length. Evaluate one of the expressions
when x = 8.
303(8) + 6 ==3x + 6
The length of a side of the table is
30 inches.
ANSWER

12. 1.6Guided Practice
The expressions 8y° and ( 9y – 15 )° represent the
measures of two of the angles in the table in
Example 3. Find the measure of an angle.
3.
120o
ANSWER

13. 1.6Exit Slip
1. Draw a convex hexagon.
ANSWER
quadrilaterals ; not regularANSWER
2. This figure shows the tiles on a kitchen floor.
What type of polygon are the tiles? Are they
regular polygons?

14. 1.6
3. This figure is a regular polygon.
Find the length of each side.
ANSWER 16 cm
Exit Slip

15. 1.6
Homework
Pg 44-47
#21, 25, 29, 32, 41