Download Pearson Geometry 6.1.notebook

Pearson Geometry 6.1.notebook
January 31, 2017
BELL RINGER
1. What is the sum of the measures of the angles of a triangle?
2. What is the sum of the measures of the angles of a rectangle?
1
Pearson Geometry 6.1.notebook
January 31, 2017
Polygon Angle­Sum Theorems
In the bell ringer, we knew that the sum of all three angles of a triangle is 180.
We also know that the sum of the angles of a rectangle is 360.
Using triangles, we can determine what the sums of the angles of any polygon will be.
Quadrilateral ­ 4 sides
2 triangles
180 + 180 = 360
Pentagon ­ 5 sides
3 triangles
180 + 180 + 180 = 540
Hexagon ­ _____ sides
______ triangles.
Sum of the angles = ________
2
Pearson Geometry 6.1.notebook
January 31, 2017
Instead of having to draw a polygon each time and then divide it into the triangles to determine the sum of the angles of the polygon, there is a simpler way of doing this.
Polygon Angle­Sum Theorem ­ The sum of the measures of the interior angles of an n­gon is ** n is the number of sides of the polygon.
What is the sum of the measures of the interior angles of a heptagon?
A heptagon is a 7­sided figure so n = 7. So the sum of the interior angles of a heptagon is 900.
Find the sum of the interior angles of a 17 ­ gon.
3
Pearson Geometry 6.1.notebook
January 31, 2017
The sum of the interior angle measures of a polygon is 1980. How many sides does the polygon have? Use the same formula and solve for n.
Equilateral Polygon ­ Polygon with all sides congruent.
Equiangular Polygon ­ Polygon with all angles congruent.
Regular Polygon ­ Polygon that is both equilateral and equiangular.
Corollary to the Polygon Angle­Sum Theorem ­ The measure of each interior angle of a regular n­gon is
The common housefly has eyes that consists of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle of a regular hexagon?
Find the measure of each interior angle of a regular nonagon.
4
Pearson Geometry 6.1.notebook
January 31, 2017
How many sides does a pentagon have?
What is the sum of all the interior angles?
Find angle Y.
Find in quadrilateral EFGH.
Find the measures of Find the measures of For each figure, what do the exterior angles add up to?
5
Pearson Geometry 6.1.notebook
January 31, 2017
Polygon Exterior­Angle Sum Theorem ­ The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
It does not matter the number of sides, the sum of the measures of the exterior angles is always 360.
What is the measure of an exterior angle of a regular nonagon? 6
Pearson Geometry 6.1.notebook
January 31, 2017
The measure of an exterior angle of a regular polygon is 60. Find the measure of the interior angle and the number of sides.
P. 356 7 ­ 37, 41
7
Pearson Geometry 6.1.notebook
January 31, 2017
P. 356 7 ­ 37, 41
8