Classifying Quadrilaterals
Pacing:This lesson should take one to two class periods
Goal: Students are introduced to the most common quadrilaterals and relationships they share. A Venn diagram
is provided as a visual to allow students to visualize how a quadrilateral such as a square fits with a rectangle,
parallelogram, and trapezoid.
Have students take the Venn diagram and transfer it to a hierarchy, showing the most general quadrilateral to the
most specific quadrilateral.
Discussion! Begin a discussion with students regarding trapezoids and parallelograms. Some textbooks describe
a trapezoid as, “a quadrilateral with at least one pair of parallel sides.” Discuss this possible definition with your
students. How would the Venn diagram change if this definition were accepted as true? Should it be accepted as
true? Why is the definition of a trapezoid provided in this text stating “exactly one pair of parallel sides?”
Additional Examples:Ask students to answer the following questions, either on a personal whiteboard, journal entry,
or in a Think-Pair-Share group.
a.Always, sometimes, never.All rhombi are squares.Sometimes. A square is a special type of rhombus.
b.Always, sometimes, never.All rhombi are parallelograms.Always.
c.Always, sometimes, never.Parallelograms are trapezoids.This answer depends upon the discussion of your
class.Pythagorean’s Theorem AGAIN!Reiterate to your students the connection between Pythagorean’s Theorem and the
distance formula. This is especially helpful when determining the lengths of segments of a quadrilateral to determine
its appropriate classification.
Trapezoids and Parallel Lines!Encourage your students to make the connection between consecutive interior angles
of parallel lines and a trapezoid. A trapezoid is really a pair of parallel lines cut by two transversals. Therefore,
consecutive interior angles are supplementary (according to Euclid’s’ 5thPostulate).
Using Parallelograms
Pacing:This lesson should take one class period
Goal:The purpose of this lesson is to familiarize students with properties special to parallelograms. These properties
are useful when proving a figure is a parallelogram. These properties also hold for rectangles, rhombi, and squares
- those quadrilaterals that are “included” within parallelograms in the Venn diagram.
In-class Activity!Instead of using string, your students can also use raw spaghetti noodles. Be sure the segments are
equal in length; otherwise, the models may not illustrate a parallelogram appropriately.
Making Connections! Make as many connections as possible. This will help your students see how geometrical
concepts fit together. For example, students have learned parallel lines are equidistant from each other. Connect this
to a parallelogram
Flash Fast Game!Have your students create flashcards with quadrilateral names on one side and important infor-
mation or properties on the reverse. Have various types of quadrilaterals, both abstract and real world, ready to show
students. Once students believe they have classified the quadrilateral, they are to hold up the appropriate name. You
can keep score or use this as a summative assessment.
1.6. Quadrilaterals