Chapter 3.4 Polygons Day 1 .notebook October 30, 2013
DIRT
Identify the relation of the angle pairs: 1) <1 and <9 ______2) <2 and <7 ______3) <7 and <11 ______4) <9 and <16 ______5) <1 and <4 ______6) <6 and <11______7)<9 and <11______
8) Find the value of x to prove l // m
55 l
x+25 m
1 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013
3.4 The Polygon AngleSum Theorems
Objective: To classify polygons To find the sums of the measures of the interior and exterior angles of polygons M.2.B. Performance Standard 3.6 DOK1 Knowledge MA 3
2 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013
Polygon A closed plane figure with at least 3 sides that are segments. The sides intersect only at their endpoints and no adjacent sides are collinear.
examples: counterexample:
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Polygons
# of sides type
3
4
5
6
7
8
9
10
n
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Naming a polygon Start at any vertex and list vertices consecutively.
A
R L
B G
E
List the vertices:
List the sides:
List the angles:
Name: ALGEBR
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Concave: when any part of the diagonals fall on the outside of the polygon.
Hmmmmmm ... Can a triangle be convex? Concave??? Why??
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Remember equiangular?? What about equilateral?
When a polygon is both equiangular AND equilateral, we call it REGULAR.
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Classify the polygon. Use three words if possible.
Ex 1) Ex 2)
Ex 3) Ex 4)
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Classify the polygon. Use three words if possible.
Ex 5) Ex 6)
Ex 7)
70 70
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Sketch the polygon if possible.
Ex 8) Regular hexagon
Ex 9) Equilateral right triangle
Ex 10) Concave equiangular qualdrilateral
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Exploration: Triangles and polygons
Using the dot paper provided, work with your desk partner and sketch each polygon.
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Fill out the chart on your paper.
Type of # of sides # of triangles Sum of the interior angles polygon
triangle
hexagon
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What conjectures can you make about the relationship between the number of sides of a polygon and the sum of the interior angles (1st and 4th column)? (Hint: think about patterns)
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Worksheet Guide for p147-150 1-10, 55, 71-73, 80-86
1. Is the figure a polygon?______If not, why? ______
2. Is the figure a polygon?______If not, why? ______
3. Is the figure a polygon?______If not, why? ______
4. Is the figure a polygon?______If not, why? ______
5. Name of polygon: ______6. Name of polygon: ______Sides: ______Sides: ______Angles: ______Angles: ______
7. Name of polygon: ______8. Classify by sides: ______Sides: ______Convex or concave? ______Angles: ______9. Classify by sides: ______Convex or concave? ______
10. Classify by sides: ______Convex or concave? ______
55. Provide 4 sentences to describe the figure. ______
______
______
______
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71. Work: ______72. Work: ______
y= ______x= ______
73. Work: ______80. opposite rays: ______
81. two right angles: ______
82. two segments: ______
x= ______83. an acute angle: ______
y= ______
84. an obtuse angle: ______
85. a straight angle: ______
86. a midpoint: ______
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