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 \begin{align*} \ || \ \end{align*} | Diagonals bisect each other | Diagonals \begin{align*}\perp\end{align*} | Opposite sides \begin{align*}\cong\end{align*} | Opposite angles \begin{align*}\cong\end{align*} | Consecutive Angles add up to \begin{align*}180^\circ\end{align*} | |
---|---|---|---|---|---|---|
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 \begin{align*}138^\circ\end{align*}.
Texas Instruments Resources
In the CK-12 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.