Name
LESSON
Date
Class
Problem Solving
9-5 Classifying Polygons
Write the correct answer.
The drawing shows a crown designed by a child in an arts and
crafts class. The crown is composed of 4 different figures.
1. Name the polygon in figure 1.
2. Name the polygon in figure 4.
1
2 3 4
3. Name the polygon in figure 3.
5. Name the polygon formed by figures
2, 3, and 4.
4. Is the crown a regular polygon?
Explain.
Choose the letter for the best answer.
The box shows some basic shapes from a word processing tool bar.
6. Which figure is not a quadrilateral?
A Figure 2
C Figure 4
B Figure 3
D Figure 5
1
2
3
7. Which figure is not a polygon?
F Figure 3
H Figure 11
J Figure 12
G Figure 9
4
5
6
8. Which figure is a pentagon?
A Figure 4
C Figure 10
B Figure 5
D Figure 12
7
8
9
9. Which figure is a regular polygon?
F Figure 1
H Figure 7
G Figure 2
J Figure 8
10
11
12
10. Which figure is an octagon?
C Figure 11
A Figure 6
B Figure 10
D Figure 12
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Holt Mathematics
Problem Solving
9-5 Classifying Polygons
Challenge
9-5 The Diagonal Count
LESSON
LESSON
Write the correct answer.
Consecutive vertices connect the sides of
a polygon. A diagonal of a polygon is a
segment that connects two nonconsecutive
vertices.
The drawing shows a crown designed by a child in an arts and
crafts class. The crown is composed of 4 different figures.
diagonals
1. Name the polygon in figure 1.
The figure shows two diagonals of a pentagon.
decagon
Other diagonals can be drawn in the
pentagon from other vertices.
2. Name the polygon in figure 4.
For each polygon below, find the total
number of diagonals from all the vertices. Do not count the
same diagonal more than once. Hint: Draw each figure and then
draw all possible diagonals. Use different colors to distinguish
the diagonals as the number of sides of the polygons
increases.
1. Triangle
0 diagonals
2 3 4
3. Name the polygon in figure 3.
pentagon
5. Name the polygon formed by figures
2, 3, and 4.
4. Is the crown a regular polygon?
Explain.
2 diagonals
2. Quadrilateral
1
hexagon
pentagon
No, sides and angles
not congruent.
Choose the letter for the best answer.
The box shows some basic shapes from a word processing tool bar.
5 diagonals
3. Pentagon
5. Heptagon
9 diagonals
4. Hexagon
14 diagonals
6. Octagon
20 diagonals
6. Which figure is not a quadrilateral?
A Figure 2
C Figure 4
B Figure 3
D Figure 5
1
2
3
7. Which figure is not a polygon?
F Figure 3
H Figure 11
J Figure 12
G Figure 9
4
5
6
8. Which figure is a pentagon?
A Figure 4
C Figure 10
B Figure 5
D Figure 12
7
8
9
9. Which figure is a regular polygon?
F Figure 1
H Figure 7
G Figure 2
J Figure 8
10
11
12
10. Which figure is an octagon?
C Figure 11
A Figure 6
B Figure 10
D Figure 12
45
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
46
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Puzzles, Twisters & Teasers
9-5 Bean Me Up, Scotty!
Reading Strategies
9-5 Compare and Contrast
LESSON
LESSON
Regular Polygon
A polygon is a closed, plane figure
formed by three or more line segments.
Irregular Polygon
Decide whether or not each figure is a polygon. Circle the letters
next to your answers. Unscramble the letters to solve the riddle.
1.
A regular polygon has sides of equal
length, and all angle measures are the same.
2.
Compare the regular and irregular polygons.
Answer each question.
1. How many sides do both shapes have?
2. How many angles do both shapes have?
5 sides
5 angles
polygon L
3. How are the two polygons alike?
not polygon P
3.
polygon A
not polygon D
polygon P
not polygon E
polygon N
not polygon E
4.
Both polygons have 5 sides and 5 angles
4. How are the two polygons different?
Regular polygons have sides and angles of equal length,
but irregular polygons do not.
polygon M
not polygon C
Compare this regular octagon and regular pentagon.
Regular Pentagon
5.
Regular Octagon
6.
polygon T
5. Compare the number of sides and angles in a pentagon to the
number of sides and angles in an octagon.
A pentagon has 5 sides and angles and an octagon has 8 sides
not polygon A
What type of beans do llamas eat?
and angles.
L
6. How are the octagon and pentagon alike?
L
A
M
A
B
E
A
N
S
Possible answer: They each have sides of equal length and angles of
equal measure.
7. How are the octagon and pentagon different?
The number of sides and angles are different for each polygon.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
47
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
106
48
Holt Mathematics
Holt Mathematics