Download 3.1.5.4 Trapezoids

Project AMP
Dr. Antonio Quesada – Director, Project AMP
Properties of Special Parallelograms
Lab Summary:
This lab consists of four activities that lead students through the construction of a trapezoid.
Students then explore the shapes, making conclusions about the angles, diagonals, and sides of the shapes.
Key Words:
trapezoid
Background Knowledge:
Students should be familiar with the basic geometry software commands. This lab does not
provided step by step instructions for constructing a trapezoid. Therefore, students should understand that
to construct a trapezoid, parallel lines must be constructed first to serve as the bases of a trapezoid. To
construct the legs, students then must construct segments connecting the parallel lines.
Learning Objectives:
Students will identify the basic properties of trapezoids.
Materials:
Geometry software
Suggested procedure:
Split students into groups of two or three. Pass out worksheets
Assessment:
Check the completed worksheets and student constructions.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Trapezoids
Team members’ names: __________________________________________________
File name: ____________________________________________________________
Goal: Construct a trapezoid and analyze some of it properties.
1. This lab does not give you step by step instructions. Using your prior Cabri skills, construct a
Trapezoid. The guidelines for a trapezoid are given below.
A trapezoid has the following properties:
• It is four sided
• Two sides are parallel
• Label the vertices K, L, M, and N
An example is shown below:
2. In your own words, explain how you constructed this trapezoid:
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The parallel sides of the trapezoid are called the bases and the nonparallel sides are called the
legs. The angles at the ends of the base are called base angles.
3. What are the base angles and the sides (How many)?
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What are the leg angles and sides (How many)?
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Project AMP
Dr. Antonio Quesada – Director, Project AMP
Note: If students are not familiar with Cabri, press F1 on the keyboard. A help menu for each tool selected will appear
on the bottom of the screen.
Now, we will take a look at a special type of trapezoid called an isosceles trapezoid.
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Construct a circle and label the center of the circle P
Draw a line P and label line l.
Label the points E and F that intersect the line and the circle
Pick a point Q inside the circle, not on P.
Construct a parallel line m to line l
Label the intersection of this line and the circle points G and H.
Now construct segments EF , FG , GH , and HE .
Hide lines l and m and the circle.
[Use circle tool]
[Use the line tool]
[Use the point tool]
[Use the point tool]
[Use the parallel line tool]
[Use the point tool]
[Use hide and show tool]
Measure the sides and angles of the isosceles trapezoid and complete the chart below:
Name of Side
Length
Name of Angle
Measurement
What observations can you make about the bases, the legs and the base angles?
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Complete the following properties:
The bases of an isosceles trapezoid are always _______________________.
The legs of an isosceles trapezoid are always ______________________.
The base angles of an isosceles trapezoid are always _____________________.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Now, compare and contrast trapezoids to the other quadrilaterals.
Is a trapezoid a parallelogram (hint- defining characteristic of a parallelogram)? Why or why not?
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Is a trapezoid a kite (hint – what defines a kite)? Why or why not?
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Let’s reflect! In the space below, draw a rough sketch of each quadrilateral.
Rhombus
Parallelogram
Rectangle
Kite
Trapezoid
Square
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Note: If students are not familiar with Cabri, press F1 on the keyboard. A help menu for each tool selected will appear on the
bottom of the screen
Extension:
Compare and contrast the different kinds of quadrilaterals. Display your information as a written
summary, diagram or chart. Compare these finding to the hands-on experience with quadrilaterals,
Lab #1. Complete a final Venn Diagram or tree (similar to a family tree) showing the relationship of
the following quadrilaterals: isosceles trapezoid, kite, parallelogram, rectangle, rhombus, square, and
trapezoid.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Extension:
Using Cabri construct a Venn Diagram that shows the relationship of quadrilaterals,
parallelograms, rectangles, squares, kites, and trapezoids.
An example of a Venn Diagram is shown below.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Extension:
Using Cabri construct a Venn Diagram that shows the relationship of quadrilaterals,
parallelograms, rectangles, squares, kites, trapezoids, and isosceles trapezoids.
An example of a Venn Diagram is shown below.