Project AMP Dr. Antonio Quesada – Director, Project AMP

Properties of Special

Lab Summary: This lab consists of four activities that lead students through the construction of a . Students then explore the shapes, making conclusions about the , , 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 .

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: ______

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)? ______

What are the leg angles and sides (How many)? ______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.

1. Construct a circle and label the center of the circle P [Use circle tool] 2. Draw a line P and label line l. [Use the line tool] 3. Label the points E and F that intersect the line and the circle [Use the point tool] 4. Pick a point Q inside the circle, not on P. [Use the point tool] 5. Construct a parallel line m to line l [Use the parallel line tool] 6. Label the intersection of this line and the circle points G and H. [Use the point tool] 7. Now construct segments EF , FG , GH , and HE . 8. Hide lines l and m and the circle. [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 Measurement

What observations can you make about the bases, the legs and the base angles? ______

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 .

Is a trapezoid a (hint- defining characteristic of a parallelogram)? Why or why not? ______

Is a trapezoid a (hint – what defines a kite)? Why or why not? ______

Let’s reflect! In the space below, draw a rough sketch of each .

Rhombus Parallelogram

Kite Trapezoid

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, , 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, , , 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.