section 2.4 angle properties in polygons pages/teacher pages/margot crewe... · 2012-11-02 ·...
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2.4AnglePropertiesinPolygons.notebook
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October 24, 2012
May 910:17 AM
Section 2.4Angle Properties in Polygons
Goal: Determine properties of angles in polygons, and use these properties to solve problems.
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2.4AnglePropertiesinPolygons.notebook
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How is the number of sides in a polygon related to the sum of its interior angles and the sum of its exterior angles?
Fill in the blanks of the following chart and determine a pattern to find the sum of the interior angles of any polygon.
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PolygonNumber of
SidesNumber of Triangles
Sum of Angle Measures
Triangle 3 1 180°
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Write a conjecture for the sum of the interior angles of a polygon.
![Page 4: Section 2.4 Angle Properties in Polygons Pages/Teacher Pages/Margot Crewe... · 2012-11-02 · 2.4AnglePropertiesinPolygons.notebook 1 October 24, 2012 May 910:17 AM Section 2.4 Angle](https://reader033.vdocument.in/reader033/viewer/2022050414/5f8a668d79b30f78f4345ae8/html5/thumbnails/4.jpg)
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The formula to calculate the sum of the interior angles of a polygon is:
where n = the number of sides.
S = (n - 2) x 1800
![Page 5: Section 2.4 Angle Properties in Polygons Pages/Teacher Pages/Margot Crewe... · 2012-11-02 · 2.4AnglePropertiesinPolygons.notebook 1 October 24, 2012 May 910:17 AM Section 2.4 Angle](https://reader033.vdocument.in/reader033/viewer/2022050414/5f8a668d79b30f78f4345ae8/html5/thumbnails/5.jpg)
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Regular polygon: a polygon all of whose sides are the same length and all of whose interior angles are the same measure.
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Determine the sum of the interior angles of a regular decagon (10-sided shape).
![Page 7: Section 2.4 Angle Properties in Polygons Pages/Teacher Pages/Margot Crewe... · 2012-11-02 · 2.4AnglePropertiesinPolygons.notebook 1 October 24, 2012 May 910:17 AM Section 2.4 Angle](https://reader033.vdocument.in/reader033/viewer/2022050414/5f8a668d79b30f78f4345ae8/html5/thumbnails/7.jpg)
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What is the measure of each of a regular decagon‛s interior angles?
![Page 8: Section 2.4 Angle Properties in Polygons Pages/Teacher Pages/Margot Crewe... · 2012-11-02 · 2.4AnglePropertiesinPolygons.notebook 1 October 24, 2012 May 910:17 AM Section 2.4 Angle](https://reader033.vdocument.in/reader033/viewer/2022050414/5f8a668d79b30f78f4345ae8/html5/thumbnails/8.jpg)
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The angle sum of a polygon is 2160°. Determine the number of sides of the polygon.
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Each interior angle of a regular polygon is 162°. Show that the polygon has 20 sides.
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Determine the measure of each interior angle of a regular 15 sided polygon(pentadecagon).
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Investigating the EXTERIOR Angle Sum of Polygons
Find the exterior angles in each diagram below. (not drawn to scale)
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Use inductive reasoning to make a conjecture about the exterior angle sum of a polygon.
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Use deductive reasoning to prove your conjecture.
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Example Proof (Can be extended for any polygon)
Given: ΔABCProve:
Statement Justification
Supplementary Angles formed by Straight Line
Addition Property
Triangle Sum Theorem
Subtraction Property
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Convex Polygon: a polygon in which each interior angle measures less than 1800.
Concave Polygon (non-convex): a polygon with one or more interior angles greater than 1800.
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A floor tiler designs custom floors using tiles in the shape of regular polygons. Can a tiling pattern be created using regular hexagons and equilateral triangles that have the same side length? Explain.
Sum of angles in a hexagon: S = 180(n - 2)= 180(6 - 2)= 180(4)= 7200
Each angle in a regular hexagon: 7200÷6 = 1200
Each angle in a equilateral triangle is 600.
Two hexagons and two triangles put together: The angle at the common vertices will be 3600.
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To summarize our results from our previous investigations:
Interior angle sum of a convex polygon:
Exterior angle sum of a convex polygon:
Interior angle of a regular convex polygon:
(n-2) x 1800 3600 (n-2) x 1800n
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2.4 Assignment: Nelson Foundations of Mathematics 11, Sec 2.4, pg, 99‐103
Questions: 1‐5, 7‐9, 11, 13, 14, 16