Name__________________________________ Date_______________ Period_____ Geometry w/ Trig.
1.6 Two-Dimensional Figures
PART A: Use your notes to complete the general description of a polygon below. Read it carefully.
A polygon is a __ __ __ __ __ __ figure formed by segments called __ __ __ __ __.
Each side intersects exactly two other sides at their __ __ __ __ __ __ __ __ __.
In other words, a polygon cannot have an “opening” and segments cannot “crisscross.”
Example 1: Identifying Polygons
State whether the figure is a polygon. If it is not, explain why.
Solution:
Figure A is a polygon.
Figure B is not a polygon. It only has two sides, and it has a side that is not a segment (curved!).
Figure C is a polygon.
Figure D is not a polygon. Two of the sides intersect only one other side (not completely enclosed!).
Figure E is not a polygon. Some of its sides intersect more than two other sides (two segments crisscross!)
PRACTICE:
Is the figure a polygon? If no, explain why.
1.
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2.
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3.
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4.
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PART B: Use your notes to complete the description of convex and concave. Read it through carefully.
Suppose the line containing each side is drawn. If any of the lines contain any
point in the __ __ __ __ __ __ __ __ of the polygon, then the polygon is
__ __ __ __ __ __ __. It will appear as if two or more of the sides “cave in”.
A polygon is __ __ __ __ __ __ if it is not concave. If you extend any side
of the polygon, that line should never pass through the interior of the polygon.
Example 2: Identifying Convex and Concave Polygons
State whether each polygon is convex or concave.
a)
Convex
When the sides are extended, none of
them cross through the interior.
b)
Concave
When the sides are extended, some of
them cross through the interior.
You also do not see any sides
You can also see the left and right
“caving in”.
of the polygon “caving in”.
sides
PRACTICE:
State whether the polygon is convex or concave.
5.
6.
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7.
____________
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PART C: Use your notes to complete the description of equilateral, equiangular, regular, and irregular.
Read it through carefully.
An __ __ __ __ __ __ __ __ __ __ __ polygon has all sides __ __ __ __ __ __ __ __ __,
but an __ __ __ __ __ __ __ __ __ __ __ polygon has all __ __ __ __ __ __ congruent.
A __ __ __ __ __ __ __ polygon is a __ __ __ __ __ __ polygon that is both equilateral and equiangular.
(Remember that a regular polygon is only convex - never concave!).
If the polygon is not regular, then it is considered __ __ __ __ __ __ __ __ __.
Example 3: Classifying Polygons
Classify each polygon with its BEST description: equilateral, equiangular, regular, or irregular.
a)
Equilateral
(only all sides are congruent)
a)
b)
Regular
(all sides and all angles are
congruent)
PRACTICE:
Decide if the polygon is best described as equilateral, equiangular, regular, or irregular.
8.
9.
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PART D: Use the following chart for part (a) of the practice problems.
Be sure to first read through the detailed directions and the example problem below.
Number of Sides
3
4
5
6
7
Number of Sides
8
9
10
12
n
Type of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Type of Polygon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
Example 4: Describing Polygons
a)
b)
c)
d)
Name the polygon – List the vertices consecutively (i.e. “in order”). You may start with any vertex.
State the type of polygon - Use the chart above.
Decide if the polygon is convex or concave.
Decide if the polygon is best described as equilateral, equiangular, regular, or irregular.
Solution:
a)
b)
c)
d)
CDEAB (or ABCDE, EDCBA, etc) not ACEBD!!
Pentagon (5 sides)
Convex (no sides “cave in”)
Irregular (sides and angles are not all congruent)
PRACTICE: Follow the directions listed above for each polygon pictured.
10. a)
11. a)
B
b)
b)
c)
c)
d)
d)
J
12. a)
T
b)
c)
c)
L
d)
d)
S
W
14. a)
c)
E
F
D
G
A
C
B
K
R
B
15. a)
S
V
T
Q
d)
Y
13. a)
b)
M
b)
F
A
c)
U
G
C
H
J
d)
P
P
H
C
A
b)
G
I
E
D
PART E: Use any previous knowledge to complete the description of perimeter, circumference, and
area.
The perimeter of a polygon is the sum of the lengths of the __ __ __ __ __ of the polygon.
For a __ __ __ __ __ __, however, the distance around it is called the circumference.
The __ __ __ __ of a figure is the number of __ __ __ __ __ __ units needed to cover a surface.
This is why the units for area is often written as units2.
Example 5: Finding Perimeter and Area
Find the perimeter or circumference and area of the figure.
PRACTICE:
Find the perimeter or circumference and area of the figures below.
Show all work, including the formula, and round to the nearest tenth.
Circle your answers and remember units!
1.
2.
6 ft
3.
4.