Chapter 6: Polygons and Quadrilaterals
Introduction
This chapter starts with the properties of polygons and narrows to focus on quadrilaterals. We will study several different types of quadrilaterals: parallelograms, rhombi, rectangles, squares, kites and trapezoids. Then, we will prove that different types of quadrilaterals are parallelograms or something more specific.
 6.1.
Interior Angles in Convex Polygons
 6.2.
Exterior Angles in Convex Polygons
 6.3.
Parallelograms
 6.4.
Quadrilaterals that are Parallelograms
 6.5.
Parallelogram Classification
 6.6.
Trapezoids
 6.7.
Kites
 6.8.
Quadrilateral Classification
Chapter Summary
Summary
This chapter starts by introducing interior and exterior angles in polygons. Then, all special types of quadrilaterals are explored and classified, both on and off the coordinate plane.
Chapter Keywords
 Polygon Sum Formula
 Equiangular Polygon Formula
 Regular Polygon
 Exterior Angle Sum Theorem
 Parallelogram
 Opposite Sides Theorem
 Opposite Angles Theorem
 Consecutive Angles Theorem
 Parallelogram Diagonals Theorem
 Opposite Sides Theorem Converse
 Opposite Angles Theorem Converse
 Consecutive Angles Theorem Converse
 Parallelogram Diagonals Theorem Converse
 Rectangle Theorem
 Rhombus Theorem
 Square Theorem
 Trapezoid
 Isosceles Trapezoid
 Isosceles Trapezoid Diagonals Theorem
 Midsegment (of a trapezoid)
 Midsegment Theorem
 Kite
 Kite Diagonals Theorem
Chapter Review
Fill in the flow chart according to what you know about the quadrilaterals we have learned in this chapter.
Determine if the following statements are sometimes, always or never true.
 A trapezoid is a kite.
 A square is a parallelogram.
 An isosceles trapezoid is a quadrilateral.
 A rhombus is a square.
 A parallelogram is a square.
 A square is a kite.
 A square is a rectangle.
 A quadrilateral is a rhombus.
Table Summary
Determine if each quadrilateral has the given properties. If so, write yes or state how many sides (or angles) are congruent, parallel, or perpendicular.
Opposite sides 
Diagonals bisect each other 
Diagonals 
Opposite sides 
Opposite angles 
Consecutive Angles add up to 


Trapezoid  
Isosceles Trapezoid  
Kite  
Parallelogram  
Rectangle  
Rhombus  
Square 
Find the measure of all the lettered angles below. The bottom angle in the pentagon (at the bottom of the drawing) is
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9691.