Classifying Polygons

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Classifying Polygons
PRE-ALGEBRA LESSON 9-3
(For help, go to Lesson 9-2.)
For the angle measures given, classify the angle
as acute, right, or obtuse. 1. 85 2. 95 3. 16
0 4. 90 5. 36 6. 127
Check Skills Youll Need
9-3
2
Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Solutions 1. acute 2. obtuse 3. obtuse 4. ri
ght 5. acute 6. obtuse
9-3
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Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Classify the triangle by its sides and angles.
The triangle has no congruent sides and one
obtuse angle.
The triangle is a scalene obtuse triangle.
Quick Check
9-3
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Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Name the types of quadrilaterals that have at
least one pair of parallel sides.
All parallelograms and trapezoids have at least
one pair of parallel sides.
Parallelograms include rectangles, rhombuses, and
squares.
Quick Check
9-3
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Classifying Polygons
PRE-ALGEBRA LESSON 9-3
A contractor is framing the wooden deck shown
below in the shape of a regular dodecagon (12
sides). Write a formula to find the perimeter of
the deck. Evaluate the formula for a side length
of 3 ft.
To write a formula, let x the length of each
side.
The perimeter of the regular dodecagon is   x
x x x x x x x x x x x.
Therefore a formula for the perimeter is P 12x.
P 12x Write the formula.
12(3)   Substitute 3 for x.
36 Simplify.
Quick Check
For a side length of 3 ft, the perimeter is 36 ft.
9-3
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Classifying Polygons
PRE-ALGEBRA LESSON 9-3
Name the following. 1. a type of triangle that
has at least two congruent sides and one right
angle 2. a type of quadrilateral that can have
opposite sides parallel and no right angles
3. Write a formula for the perimeter of a
regular heptagon (7 sides). Evaluate for a side
of 12 in.
isosceles right triangle
parallelogram, rhombus
P 7x 84 in.
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Problem Solving Strategy Draw a Diagram
PRE-ALGEBRA LESSON 9-4
Draw several different quadrilaterals. Connect
the midpoints of the sides of each figure. Write
a sentence explaining in what way the figures
inside the quadrilaterals are alike.
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Problem Solving Strategy Draw a Diagram
PRE-ALGEBRA LESSON 9-4
(For help, go to Lesson 9-3.)
Sketch each figure. 1. equilateral
triangle 2. rectangle 3. pentagon 4. hexagon 5.
octagon
Check Skills Youll Need
9-4
9
Problem Solving Strategy Draw a Diagram
PRE-ALGEBRA LESSON 9-4
9-4
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Problem Solving Strategy Draw a Diagram
PRE-ALGEBRA LESSON 9-4
How many diagonals does a nonagon have?
9-4
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Problem Solving Strategy Draw a Diagram
PRE-ALGEBRA LESSON 9-4
(continued)
You can organize your results as you count the
diagonals. Do not count a diagonal twice. (The
diagonal from A to C is the same as the one from
C to A.) Then find the sum of the numbers of
diagonals.
Vertex
Number of Diagonals
6
A
6
B
5
C
4
D
E
3
F
2
G
1
H
0
I
0
Total
27
A nonagon has 27 diagonals.
Quick Check
9-4
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Problem Solving Strategy Draw a Diagram
PRE-ALGEBRA LESSON 9-4
Solve. 1. How many diagonals does a
quadrilateral have? 2. How many triangles can
you form if you draw all the diagonals from one
vertex of a pentagon? 3. How many triangles
can you form if you draw all the diagonals of a
rectangle?
2 diagonals
3 triangles
8 triangles
9-4