Download H. Geo Unit 6

Polygons and Quadrilaterals
Honors Geometry Unit 6
Warm Up for 1/31
• Fill in the missing angle measures and add up all the angles in the figure.
Do you notice a pattern between number of sides and the sum?
Polygons
• A Polygon is any closed plane figure made by 3 or more sides
• Plane Figure:
• Closed Figure:
• Examples:
Classifying Polygons
• We can classify all polygons into several categories
• Classifying by shape:
• Convex Polygons:
• Concave Polygons:
Classifying Polygons
• Classifying by Side or Angle Properties:
• Equilateral Polygon:
• Equiangular Polygon:
• Regular Polygon:
Classifying Polygons
• Classifying by Side or Angle Properties:
Classifying Polygons
• Classifying by Number of Sides
•3
—4
•5
—6
•7
—8
•9
—10
• 11+
Polygons
• Polygon Angle Sum-Theorem
• Thinking about the bell work, how did the number of triangles drawn relate to
the number of sides?
• What do the angles of a triangle add up to?
Polygons
• Polygon Angle-Sum Theorem
• The sum of the interior angles of any convex polygon can be found using the
Polygon Angle-Sum Theorem
Polygons
• What is the sum of the interior angles of a heptagon?
• Of a 17-gon?
• Of a 102-gon?
Polygons
• If the sum of the interior angles of a polygon is 1980°, how many
sides does the polygon have?
Warm Up for 2/1
1. What is the sum of the interior angles of a convex nonagon?
2. What is the sum of the interior angles of a convex 23-gon?
3. How many sides does a convex polygon have if the sum of the
interior angles is 3960°? If the sum is 9720°?
Regular Polygons
• Because all the angles of a Regular Polygon are congruent, we can
find the measure of each interior angle:
Regular Polygon
• What is the measure of each interior angle of a regular Pentagon?
• Of a regular 12-gon?
Using the Theorem
Using the Theorem
Using the Theorems
• Find the missing angle measures
Using the Theorems
• Solve for the variables, then find the angle measures
Using the Theorems
• Solve for the variables, then find the angle measures
Exterior Angles
• Find the Sum of the Exterior Angles of each polygon
Exterior Angles
Exterior Angles
• How could we figure out the measure of each exterior angle of a regular n-gon?
Exterior Angles
• What is the measure of an exterior angle of a regular pentagon?
• Of a regular nonagon?
• Of a regular 18-gon?
• Each polygon is a regular polygon, solve for the
variables
Exit Card