This lesson is designed to introduce students to quadrilaterals. Included in this lesson are
discussions of parallelograms, rectangles, and trapezoids.

Objectives

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.

Standards Addressed:

Grade 3

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 4

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 5

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Fifth Grade

Geometry

Classify two-dimensional figures into categories based on their properties.

Fourth Grade

Geometry

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Geometry

Congruence

Experiment with transformations in the plane

Understand congruence in terms of rigid motions

Third Grade

Geometry

Reason with shapes and their attributes.

Grades 6-8

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Use visualization, spatial reasoning, and geometric modeling to solve problems

Grades 9-12

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Technical Mathematics I

Geometry and Measurement

Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

Geometry and Measurement

Competency Goal 1: The learner will use properties of geometric figures to solve problems.

Reason for Alignment: Quadrilaterals is designed to introduce students to quadrilaterals through discussions of parallelograms, rectangles, and trapezoids. The worksheet associated with this lesson is particularly helpful with the definitions of the various kinds of quadrilaterals. This lesson provides extra practice with all the vocabulary that goes with geometry. This lesson is a reinforcement of key terms and concepts from the textbook.

Two figures are congruent to one another if they have the same size and shape

parallel

Lines that are in the same plane that do not intersect

parallelogram

A quadrilateral that contains two pairs of parallel sides

polygon

A closed plane figure formed by three or more line segments that do not cross over each other

quadrilateral

A polygon that has four sides

rectangle

A parallelogram with four right angles

rhombus

A parallelogram with four congruent sides

right angle

An angle of 90 degrees

square

A parallelogram with four congruent sides and four right angles

trapezoid

A quadrilateral with exactly one pair of parallel sides

Lesson Outline

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.

Objectives

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, called quadrilaterals.

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.

Try an example with your students, letting the students direct your moves.

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.

Closure

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.

Alternate Outline

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.

Suggested Follow-Up

Length, Perimeter, and Area: Introduces students to finding the length, perimeter, and area or two dimensional figures.

Surface Area and Volume : A lesson that introduces students to determining the surface area and volume of three
dimensional figures.