8-7 Polygons Warm Up Warm Up Lesson Presentation Problem of the Day Lesson Quizzes
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8-7 Polygons
Warm UpWarm Up
Lesson Presentation
Problem of the Day
Lesson Quizzes
8-7 Polygons
Warm UpTrue or false?
1. Some trapezoids are parallelograms.
2. Some figures with 4 right angles are squares.
3. Some quadrilaterals have only one right angle.
false
true
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
polygonregular polygondiagonal
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.
There are 8 sides and 8 angles.octagon
The sides and angles appear to be congruent.regular
The shape is a closed plane figure formed by 3 or more line segments.
polygon
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?
11 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
22 Make a Plan
Make a table to look for a pattern using regular polygons.
Solve33Draw some regular polygons and divide each into triangles.
Additional Example 2 Continued
8-7 Polygons
720°
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
Reading Math
Additional Example 2 Continued
8-7 Polygons
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°.
Solve Cont.33
Additional Example 2 Continued
8-7 Polygons
Look Back44
Each angle in a nonagon is obtuse. 140° is a reasonable answer, because an obtuse angle is between 90° and 180°.
Additional Example 2 Continued
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?
11 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
22 Make a Plan
Make a table to look for a pattern using regular polygons.
Solve33Draw some regular polygons and divide each into triangles.
Check It Out: Example 2 Continued
8-7 Polygons
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°.
Check It Out: Example 2 Continued
Solve Cont.33
8-7 Polygons
Look Back44
Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°.
Check It Out: Example 2 Continued
8-7 Polygons
Standard Lesson Quiz
Lesson Quizzes
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.
2. What is the measure of each angle in a regular
dodecagon (12-sided figure)?
150°
nonagon, regular; octagon, not regular
8-7 Polygons
1. Name the polygon and tell whether it appears to be regular or not regular.
A. pentagon, not regular
B. hexagon, regular
C. heptagon, regular
D. octagon, not regular
Lesson Quiz for Student Response Systems
octagon, not regular octagon, not regular
8-7 Polygons
2. What is the measure of each angle in a regular decagon (10-sided figure)?
A. 108
B. 144
C. 150
D. 140
Lesson Quiz for Student Response Systems
octagon, not regular octagon, not regular
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