6 th grade math homework chapter 7-7 page 354 #1-8 & #23-29 (spiral review)
TRANSCRIPT
6th Grade Math HomeworkChapter 7-7
Page 354
#1-8 & #23-29(Spiral Review)
Ch 7 Learning Goal: PLANE GEOMETRY• Learn to describe the figures by using the terms of geometry (7-1)• Learn to name, measure, classify, estimate and draw angles (7-2)• Learn to understand relationship of angles (7-3)• Learn to classify the different types of lines (7-4)• Learn to classify triangles and solve problems involving angle and side
measures of triangles (7-5)• Learn to identify, classify, and compare quadrilaterals (7-6)• Learn to identify regular and not regular polygons and to find the angle
measures of regular polygons (7-7)• Learn to recognize, describe, and extend geometric patterns (7-8)• Learn to identify congruent figures and to use congruence to solve
problems (7-9)• Learn to use translations, reflections, and rotations to transform geometric
shapes (7-10)• Learn to identify line symmetry (7-11)• Learn to identify tessellations and shapes that can tessellate (7-12)
7-7 Polygons
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpTrue or false?
1. Some trapezoids are parallelograms.
2. Some figures with 4 right angles are squares.
false
true
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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, 18, or 26 people
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Today’s Learning Goal Assignment
Learn to identify regular and not regular polygons and to find the angle measures of regular polygons.
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7-7 Polygons
Vocabulary
polygonregular polygon
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7-7 Polygons
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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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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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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
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.
There are eight sides and eight angles.octagon
The sides and angles appear to be congruent.regular
The shape is a closed plane figure formed by three or more line segments.polygon
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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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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?
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 9 congruent angles.
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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
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Additional Example 2 Continued
720°
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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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Additional Example 2 Continued
Look Back44
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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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?
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.
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22 Make a Plan
Make a table to look for a pattern using regular polygons.
Solve33Draw some regular polygons and divide each into triangles.
Try This: Example 2 Continued
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7-7 Polygons
Try This: Example 2 Continued
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7-7 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°.
Try This: Example 2 Continued
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7-7 Polygons
Look Back44
Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°.
Try This: Example 2 Continued
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
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7-7 Polygons