An Introduction To Quadrilaterals
This lesson is designed to introduce students to quadrilaterals. Included
in this lesson are discussions of parallelograms, rectangles, and
Upon completion of this lesson, students will:
- have been introduced to quadrilaterals and their properties.
- have learned the terminology used with quadrilaterals.
- have practiced creating particular quadrilaterals based on specific
characteristics of the quadrilaterals.
The activities and discussions in this lesson address the following
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
- precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
- understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
- create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship
Use visualization, spatial reasoning, and geometric modeling to solve problems
- draw geometric objects with specified properties, such as side lengths or angle measures
Links to other standards.
- Geometric: Students must be able to:
- recognize the general shape of a square and a rectangle.
- recall information about angles (particularly right angles),
parallel lines, and possibly the concept of congruency.
- Technological: Students must be able to:
- perform basic mouse manipulations such as point, click and drag.
- use a browser, such as Netscape, for experimenting with the activities.
Students will need:
- Access to a browser
- pencil and paper
- Copies of supplemental materials for the activities:
This lesson introduces students to the following terms through the included discussions:
- Focus and Review
Remind students of what they learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:
- Class, you might remember that we learned about triangles before. We learned that triangles are a family of polygons and that there are different types of triangles.
- Can anyone in here tell me what some of the types of triangles are? [i.e. right triangles, isosceles triangles, scalene triangles, etc.]
- Just as the three-sided polygon, a triangle, has a family of shapes with names, four-sided polygons have names.
Let the students know what they will be doing and learning today. Say something like this:
- Today, class, we will be talking more about the four-sided figures,
- We are going to use the computers to learn about quadrilaterals, but
please do not turn your computers on or go to this page until I ask you
to. I want to show you a little about this program first.
- Teacher Input
You may choose lead the students in a short discussion about quadrilaterals.
A series of discussions will introduce students to the different
types of quadrilaterals:
Explain to the students how to do the assignment. You should model or
demonstrate it for the students, especially if they are not familiar with
how to use our computer applets.
- Open your browser to Floor Tiles in order to
demonstrate this activity to the students.
- Explain that the quadrilateral on the screen will always remain as a
quadrilateral, even though you move the sides and corners.
- Show the students that they may access information about the sides
and angles by using the Information button.
- Pass out the Worksheet to Accompany "An
Introduction To Quadrilaterals."
- Guided Practice
Try an example with your students, letting the students direct your
- Ask the students to help you create a trapezoid from the square
on the screen. As they direct your moves, have them specify which
characteristic of the trapezoid they are attempting to create.
- When the class is satisfied with the trapezoid that has been
created, show them how to gain information about the quadrilateral from
the Information button.
- Allow the students to comment on how they think the information
shows that the quadrilateral is a trapezoid. Students should
recognize that it is necessary to show that two of the lines in the
quadrilateral are parallel. This can be done several ways:
- Remind students to consider what they know about parallel lines.
If the lines are parallel, and one of the other sides acts as a
transversal, students can identify angles that should be congruent.
Remind them that angles 1 and 3 are congruent (since alternate
interior angles are congruent), and angles 1 and 2 are
supplementary (since the two angles form a linear pair), therefore angles
2 and 3 should be supplementary, if the lines are parallel.
- If your students are not familar with the properties of parallel
lines, they may prove that the lines are parallel by calculating the slope
of the lines they suspect are parallel. The Information button
contains the coordinates of each vertex. Students may use these
coordinates to find the slope of the appropriate lines.
- Independent Practice
- Allow students to work on their own and to complete the
worksheet, should you choose to provide it. Monitor the room for
questions and to be sure that the students are on the correct web site.
- Another option: Let students form several groups. Each group should design a different quadrilateral and prove that its creation
fits the desired characteristics of the specified quadrilateral. The groups
could then show the class what they created and how they showed that
the desired characteristics were present.
You may wish to bring the class back together for a discussion of the
findings. Once the students have been allowed to share what they found,
summarize the results of the lesson. Especially emphasize the importance of knowing the characteristics of the
different types of quadrilaterals.
This lesson can be rearranged in several ways if there is only one
- Groups of students may take turns creating a quadrilateral and
proving that it has the characteristics necessary to define that shape.
- Assign each group a different quadrilateral. Let the groups
take turns using the computer to create the quadrilateral and take
note of the information.
- When each group has finished, allow the groups an opportunity to
teach the class what they found and how they proved that the necessary
characteristics were present.
- The class may work together as a whole to create the quadrilaterals
suggested on the worksheet.
- Students may direct the instructor's movements and suggest
calculations that need to be done before the class.
- OR Students may take turns using the demonstration computer
to modify the quadrilateral. The whole class can make the necessary
calculations and then check them with a partner.
This lesson may be followed by:
- Length, Perimeter, and Area: Introduces
students to finding the length, perimeter, and area or two dimensional
- Surface Area and Volume: A lesson that
introduces students to determining the surface area and volume of three