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Properties of Special Parallelograms

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Properties of Special Parallelograms 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: __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 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 Angle 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 quadrilaterals. Is a trapezoid a parallelogram (hint- defining characteristic of a parallelogram)? Why or why not? __________________________________________________________________________________ __________________________________________________________________________________ Is a trapezoid a kite (hint – what defines a kite)? Why or why not? __________________________________________________________________________________ __________________________________________________________________________________ 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. .
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