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
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• 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
Warm Up for 2/2
• Solve for the variables
Quadrilaterals
• A quadrilateral is any polygon with four sides and four angles
• Quadrilaterals can be classified into 4 main groups, each with
different properties
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Parallelograms
Trapezoids
Kites
Other Quadrilaterals
Quadrilaterals
Parallelograms
• Parallelograms are quadrilaterals with two pairs of parallel sides
• Rectangles, Rhombuses, and Squares are all parallelograms
Rectangles
• Rectangles are parallelograms with 4 right angles
• They have the same properties as parallelograms
Rhombus
• A Rhombus is a parallelogram with 4 congruent sides
• A Rhombus has the same properties as a parallelogram
Square
• A Square is a parallelogram with 4 right angles and 4 congruent sides
• A square is a parallelogram, a rectangle, and a rhombus
• It has the same properties as all three of these
Trapezoid
• A Trapezoid is a quadrilateral with only one pair of parallel sides
Isosceles Trapezoids
• Isosceles Trapezoids are trapezoids with one pair of congruent sides
• The congruent sides are not parallel
Kites
• A Kite is a quadrilateral with no sets of parallel sides and two pairs of
congruent sides
• Any quadrilateral that meets none of these specifications is just a
quadrilateral