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8-7 Polygons
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
8-7 Polygons
Warm Up
True or false?
1. Some trapezoids are parallelograms.
false
2. Some figures with 4 right angles are
squares.
true
3. Some quadrilaterals have only one right
angle.
true
8-7 Polygons
Problem of the Day
Four square tables pushed together can
seat either 8 or 10 people. How many
people could 12 square tables pushed
together seat?
14, 16, or 26 people
8-7 Polygons
Learn to identify regular and not regular
polygons and to find the angle measures
of regular polygons.
8-7 Polygons
Vocabulary
polygon
regular polygon
diagonal
8-7 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.
8-7 Polygons
8-7 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.
The shape is a closed plane figure formed
by 3 or more line segments.
polygon
There are 5 sides and 5 angles.
pentagon
All 5 sides do not appear to be congruent.
not regular
8-7 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.
The shape is a closed plane figure
formed by 3 or more line segments.
polygon
There are 8 sides and 8 angles.
octagon
The sides and angles appear to be
congruent.
regular
8-7 Polygons
Check It Out: 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.
There are 4 sides and 4 angles.
quadrilateral
The sides and angles appear to be
congruent.
regular
8-7 Polygons
Check It Out: 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.
There are 4 sides and 4 angles.
quadrilateral
All 4 sides do not appear to be
congruent.
not regular
8-7 Polygons
You can divide any quadrilateral into two
triangles by drawing a diagonal, a line
segment that connects two non-adjacent
vertices. 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°.
8-7 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
t 9 congruent angles.
8-7 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.
8-7 Polygons
Additional Example 2 Continued
720°
Reading Math
The prefixes in the names of the polygons tell you
how many sides and angles there are.
tri- = three
quad- = four
penta- = five
hexa- = six
octa- = eight
8-7 Polygons
Additional Example 2 Continued
3
Solve Cont.
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°.
8-7 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°.
8-7 Polygons
Check It Out: 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.
8-7 Polygons
Check It Out: 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.
8-7 Polygons
Check It Out: Example 2 Continued
3
Solve Cont.
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°.
8-7 Polygons
Check It Out: 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°.
8-7 Polygons
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
8-7 Polygons
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°
8-7 Polygons
Lesson Quiz for Student Response Systems
1. Name the polygon and tell whether it
appears to be regular or not regular.
A. pentagon, not regular
octagon, not regular
B. hexagon, regular
C. heptagon, regular
D. octagon, not regular
8-7 Polygons
Lesson Quiz for Student Response Systems
2. What is the measure of each angle in a
regular decagon (10-sided figure)?
A. 108
B. 144
C. 150
D. 140
octagon, not regular