Download 8-7

8-7
8-7 Polygons
Polygons
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
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
Course 1
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
Course 1
8-7 Polygons
Learn to identify regular and not regular
polygons and to find the angle measures
of regular polygons.
Course 1
8-7 Polygons
Vocabulary
polygon
regular polygon
Course 1
8-7 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.
Course 1
8-7 Polygons
Remember!
An equilateral triangle has three congruent sides.
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Course 1
8-7 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°.
Course 1
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.
Course 1
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.
Course 1
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.
Course 1
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°.
Course 1
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°.
Course 1
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.
Course 1
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.
Course 1
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°.
Course 1
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°.
Course 1
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°
Course 1