Transcript polygon - DArmitage

7-7 Polygons
Warm Up
Problem of the Day
Lesson Presentation
Course 1
7-7 Polygons
Learn to identify regular and not regular
polygons and to find the angle measures
of regular polygons.
Course 1
7-7 Polygons
Insert Lesson Title Here
Vocabulary
polygon
regular polygon
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7-7 Polygons
Triangles and quadrilaterals
are examples of polygons.
A polygon is a closed
plane figure formed by
three or more line
segments. A regular
polygon is a polygon in
which all sides are
congruent and all angles
are congruent.
Polygons are named by the number of their
sides and angles.
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7-7 Polygons
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7-7 Polygons
Additional Example 1A: Identifying Polygons
Tell whether each shape is a polygon. If so,
give its name and tell whether it appears to
be regular or not regular.
A.
The shape is a closed plane figure formed
by three or more line segments.
polygon
There are five sides and five angles.
pentagon
All 5 sides do not appear to be congruent.
Not regular
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7-7 Polygons
Additional Example 1B: Identifying Polygons
Tell whether each shape is a polygon. If so,
give its name and tell whether it appears to
be regular or not regular.
B.
The shape is a closed plane figure
formed by three or more line
segments.
polygon
There are eight sides and eight angles.
octagon
The sides and angles appear to be
congruent.
regular
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7-7 Polygons
Try This: Example 1A
Tell whether each shape is a polygon. If so,
give its name and tell whether it appears to
be regular or not regular.
A.
There are four sides and four
angles.
quadrilateral
The sides and angles appear to be
congruent.
regular
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7-7 Polygons
Try This: Example 1B
Tell whether each shape is a polygon. If so,
give its name and tell whether it appears to
be regular or not regular.
B.
There are four sides and four
angles.
quadrilateral
The sides and angles appear to
be congruent.
regular
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7-7 Polygons
The sum of the interior angle measures
in a triangle is 180°, so the sum of the
interior angle measures in a
quadrilateral is 360°.
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7-7 Polygons
Additional Example 2: Problem Solving Application
Malcolm designed a wall hanging that was
a regular 9-sided polygon (called a
nonagon). What is the measure of each
angle of the nonagon?
1
Understand the Problem
The answer will be the measure of each angle
in a nonagon.
List the important information:
• A regular nonagon has 9 congruent sides and
9 congruent angles.
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7-7 Polygons
Additional Example 2 Continued
2
Make a Plan
Make a table to look for a pattern using
regular polygons.
3
Solve
Draw some regular polygons and divide
each into triangles.
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7-7 Polygons
Additional Example 2 Continued
720°
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7-7 Polygons
Additional Example 2 Continued
The number of triangles is always 2 fewer than the
number of sides.
A nonagon can be divided into 9 – 2 = 7 triangles.
The sum of the interior angle measures in a nonagon
is 7  180° = 1,260°.
So the measure of each angle is 1,260° ÷ 9 = 140°.
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7-7 Polygons
Additional Example 2 Continued
4
Look Back
Each angle in a nonagon is obtuse. 140° is a
reasonable answer, because an obtuse angle is
between 90° and 180°.
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7-7 Polygons
Try This: Additional Example 2
Sara designed a picture that was a
regular 6-sided polygon (called a
hexagon). What is the measure of each
angle of the hexagon?
1
Understand the Problem
The answer will be the measure of each angle
in a hexagon.
List the important information:
• A regular hexagon has 6 congruent sides and
6 congruent angles.
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7-7 Polygons
Try This: Example 2 Continued
2
Make a Plan
Make a table to look for a pattern using
regular polygons.
3
Solve
Draw some regular polygons and divide
each into triangles.
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7-7 Polygons
Try This: Example 2 Continued
Course 1
7-7 Polygons
Try This: Example 2 Continued
The number of triangles is always 2 fewer than the
number of sides.
A hexagon can be divided into 6 – 2 = 4 triangles.
The sum of the interior angles in a octagon is
4  180° = 720°.
So the measure of each angle is 720° ÷ 6 = 120°.
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7-7 Polygons
Try This: Example 2 Continued
4
Look Back
Each angle in a hexagon is obtuse. 120° is a
reasonable answer, because an obtuse angle is
between 90° and 180°.
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7-7 Polygons
Insert Lesson Title Here
Lesson Quiz
1. Name each polygon and tell whether it appears
to be regular or not regular.
nonagon, regular; octagon, not regular
2. What is the measure of each angle in a regular
dodecagon (12-sided figure)? 150°
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