Section 2.4 Angle Properties in Polygons Pages/Teacher Pages/Margot Crewe... · 2012-11-02 ·...
19
2.4AnglePropertiesinPolygons.notebook 1 October 24, 2012 May 910:17 AM Section 2.4 Angle Properties in Polygons Goal: Determine properties of angles in polygons, and use these properties to solve problems.
Transcript of 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 2.4Angle Properties in Polygons
Goal: Determine properties of angles in polygons, and use these properties to solve problems.
2.4AnglePropertiesinPolygons.notebook
2
October 24, 2012
Jun 212:07 PM
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.
2.4AnglePropertiesinPolygons.notebook
3
October 24, 2012
Jun 212:04 PM
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.
2.4AnglePropertiesinPolygons.notebook
4
October 24, 2012
Jun 212:09 PM
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
2.4AnglePropertiesinPolygons.notebook
5
October 24, 2012
Jun 229:09 AM
Regular polygon: a polygon all of whose sides are the same length and all of whose interior angles are the same measure.
2.4AnglePropertiesinPolygons.notebook
6
October 24, 2012
Jun 212:12 PM
Determine the sum of the interior angles of a regular decagon (10-sided shape).
2.4AnglePropertiesinPolygons.notebook
7
October 24, 2012
Jun 212:13 PM
What is the measure of each of a regular decagon‛s interior angles?
2.4AnglePropertiesinPolygons.notebook
8
October 24, 2012
Jun 229:04 AM
The angle sum of a polygon is 2160°. Determine the number of sides of the polygon.
2.4AnglePropertiesinPolygons.notebook
9
October 24, 2012
Jun 229:05 AM
Each interior angle of a regular polygon is 162°. Show that the polygon has 20 sides.
2.4AnglePropertiesinPolygons.notebook
10
October 24, 2012
Jun 229:13 AM
Determine the measure of each interior angle of a regular 15 sided polygon(pentadecagon).
2.4AnglePropertiesinPolygons.notebook
11
October 24, 2012
Jun 212:17 PM
Investigating the EXTERIOR Angle Sum of Polygons
Find the exterior angles in each diagram below. (not drawn to scale)
2.4AnglePropertiesinPolygons.notebook
12
October 24, 2012
Jun 229:32 AM
2.4AnglePropertiesinPolygons.notebook
13
October 24, 2012
Jun 212:19 PM
Use inductive reasoning to make a conjecture about the exterior angle sum of a polygon.
2.4AnglePropertiesinPolygons.notebook
14
October 24, 2012
Jun 212:22 PM
Use deductive reasoning to prove your conjecture.
2.4AnglePropertiesinPolygons.notebook
15
October 24, 2012
Jun 229:59 AM
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
2.4AnglePropertiesinPolygons.notebook
16
October 24, 2012
Jun 212:23 PM
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.
2.4AnglePropertiesinPolygons.notebook
17
October 24, 2012
Jun 2210:26 AM
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.
2.4AnglePropertiesinPolygons.notebook
18
October 24, 2012
Jun 229:14 AM
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
2.4AnglePropertiesinPolygons.notebook
19
October 24, 2012
Jun 228:39 AM
2.4 Assignment: Nelson Foundations of Mathematics 11, Sec 2.4, pg, 99‐103
Questions: 1‐5, 7‐9, 11, 13, 14, 16
