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					                                      Teacher’s Guide
                               Geometer’s Sketchpad
                              Classifying Quadrilaterals
                                 Student Worksheet
                                    Assignment 1
                               Constructing Quadrilaterals

Directions: This worksheet will guide you through the Classifying Quadrilaterals assignment.
Questions should be answered in the space provided. Sketches should be made in a new file in
Geometer’s Sketchpad. Both the file and this worksheet will be graded. Be sure to save often to
be sure not to lose any of your work.

          Open Geometer’s Sketchpad and choose File new sketch. Go to the File menu
           and choose Save As and save the file as Quad1 followed by your first initial and
           last name. (For example, I would save my file as quad1 R Grunloh.gsp)
          As you work through the constructions below, create a text box next to each
           shape to name the type of quadrilateral you created.

   1. Construct a quadrilateral.
          Drag the vertices of the quadrilaterals.
          Can you make this quadrilateral into a parallelogram?__Yes_ A square?__Yes__
          Is this quadrilateral always a parallelogram?___No___ Always a square?__No__
          In the space below, briefly explain the why or why not?
             Answers will vary. Points may be moved to create different quadrilaterals but if
             you want the sides to always be perpendicular then they must be constructed
             using perpendicular lines.

   2. Construct a parallelogram. Think about the properties that make a quadrilateral a
      parallelogram. Your construction should always maintain its parallelogram properties.
           In the space below, explain how you guaranteed that your construction would
              always be a parallelogram.
              Construct a segment (AB)
              Construct a point (C) not on the segment
              Construct a line parallel to the side AB and through the point C
              Construct side AC
              Construct a line parallel to AC through the point B
              Construct the intersection of the parallel lines, point D
              Construct the segments CD and BD
              Hide the parallel lines


                                A                    B




                                C
                                                         D




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                                  Teacher’s Guide
3. Construct a Rectangle. Think about the properties that make a quadrilateral a rectangle.
   Your construction should always maintain the properties of a rectangle.
       In the space below, explain how you guaranteed that your construction would
          always be a rectangle.
          Construct a segment (EF)
          Construct a line perpendicular to EF through point E
          Construct a point on the perpendicular line (G)
          Construct a line perpendicular to EF through point F
          Construct perpendicular to the line EG
          Construct the intersection (H) of the last two lines constructed
          Construct the segments EG, GH, and FH
          Hide the perpendicular lines
            E                         F




            G                         H




4. Construct a Rhombus. Think about the properties that make a quadrilateral a rhombus.
   Your construction should always maintain the properties of a rhombus.
       In the space below, explain how you guaranteed that your construction would
          always be a rhombus.
          Construct a segment (JK)
          Construct a circle with center J and point K on the circle
          Construct point L on the circle
          Construct segment JL
          Construct a line parallel to JK through point L
          Construct a line parallel to JL through point K
          Construct the intersection (M) of the new parallel lines
          Construct segments JL, LM, and KM
          Hide the circle and the parallel lines
            J                     K




                           L                      M




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                                  Teacher’s Guide
5. Construct a Square. Think about the properties that make a quadrilateral a square. Your
   construction should always maintain the properties of a square.
       In the space below, explain how you guaranteed that your construction would
          always be a square.
          Construct a segment (NO)
          Select segment NO and point O and mark point N as the center of rotation
                  (double click on N or select N and choose Transform-Mark Center)
          Rotate 90 degrees (O’)
          Construct a line perpendicular to O’N through point O’
          Construct a line perpendicular to ON through point O
          Construct the intersection of the two new perpendicular lines (P)
          Construct segments O’P and OP
          Hide the perpendicular lines

            O'                P




            N                 O



6. Construct a Trapezoid. Think about the properties that make a quadrilateral a trapezoid.
   Your construction should always maintain the properties of a trapezoid.
       In the space below, explain how you guaranteed that your construction would
          always be a trapezoid.
          Construct a segment (QR) and a point not on the segment (S)
          Construct a line parallel to QR through the point S
          Construct a point (T) on this new line
          Construct the three missing sides
          Hide the parallel line

                  Q                            R



            S

                                                     T




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                                  Teacher’s Guide
7. Construct an Isosceles Trapezoid. Think about the properties that make a quadrilateral
   an isosceles trapezoid. Your construction should always maintain the properties of an
   isosceles trapezoid.
        In the space below, explain how you guaranteed that your construction would
           always be an isosceles trapezoid.
           Construct a segment (WX) and a point not on the segment (Y)
           Construct a line parallel to WX through the point Y
           Construct the segment WY
           Construct the midpoint (U) of WX
           Construct a line perpendicular to WX through the midpoint U
           Select the segment WY and the endpoints W and Y
           Mark the perpendicular line as the mirror
           Transform-Reflect
           Construct the segment YY’
           Hide the parallel line, perpendicular line, and the midpoint U

                W                              X




            Y                                          Y'




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                                        Teacher’s Guide
                                Geometer’s Sketchpad
                               Classifying Quadrilaterals
                                     Assignment 2
                                    Identifying Quadrilaterals

      Open your file created in Assignment one.
      Choose File/Save As/ and save the file as quad2 followed by your first initial and last
       name.
      Using your selection tool (the arrow), highlight a box around your entire sketch. Choose
       Display/Hide Labels
      Using the Test Tool, click on the bottom side of each quadrilateral. This will create a
       label for the bottom side. Double click on this label and change the label to read QUAD
       and a number 1-7 (Number these in some random order). At the bottom of this sheet,
       write the label in your file that corresponds to each shape.
      Delete all text boxes that label your quadrilaterals (rectangle, square, etc)
      Using the selection tool, drag the vertices of each quadrilateral so that each quadrilateral
       appears to be a square.
      Move the quadrilaterals so that they are in numerical order. (The easiest way to move the
       quadrilaterals would be to use the selection tool and select all points and segments in the
       quadrilateral and then drag the quadrilateral.)
      Save your file.
      Complete the Student Worksheet for assignment 2 and turn it in along with this page.




My File Name is _QUAD2 R Grunloh.gsp________________

My quadrilaterals are labeled as:

My Quadrilateral is QUAD_3_

My Parallelogram is QUAD_2_

My Rectangle is QUAD_6_

My Rhombus is QUAD_7_

My Square is QUAD_1_

My Trapezoid is QUAD_5_

My Isosceles Trapezoid is QUAD_4_




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                                       Teacher’s Guide
                                 Geometer’s Sketchpad
                                Classifying Quadrilaterals
                                   Student Worksheet
                                      Assignment 2
Directions: Open three of your classmates files and determine the more specific names of their
quadrilaterals and answer the questions below.
                                 File Name:              File Name:             File Name:

Quadrilateral               Answers will Vary
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid

Based on your observations in both Assignment one and Assignment two, describe the properties
that helped you identify the following shapes.
                                        Answers will vary
     Parallelogram
               Opposite sides are always parallel but not always congruent. Angles are not
               always right angles.

      Rectangle
             Opposite sides are always parallel and adjacent sides are always perpendicular (or
             make right angles). All sides are not always congruent

      Rhombus
            Opposite sides are always parallel and all sides are congruent. Angles are not
            always right angles

      Square
                Opposite sides are always parallel and adjacent sides are always perpendicular
                (for right angles). All sides are always congruent.

      Trapezoid
             Only one set of sides are always parallel (**Worth noting – by definition a
             trapezoid may not be a parallelogram although this sketch allows that)

      Isosceles Trapezoid
               Only one set of sides are always parallel (**Worth noting – by definition a
               trapezoid may not be a parallelogram although this sketch allows that) The
               nonparallel sides are always congruent


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                                     Teacher’s Guide
                              Geometer’s Sketchpad
                             Classifying Quadrilaterals
                                Student Worksheet
                                   Assignment 3
                                  Quadrilaterals Properties
     Open your original quadrilateral file
     Resave the file as Quad3 followed by your first initial and last name.
     Construct the diagonals of the different quadrilaterals.
     Experiment with the different quadrilaterals and complete the chart below.
          Measure segments and angles to help you.
          But an X in each box that is true for each quadrilateral.
     Save your file with the calculations and measurements displayed.

                                                                                   Isosceles
                   Parallelogram Rectangle Rhombus Square Trapezoid
                                                                                   Trapezoid
  Both Sets of
Opposite Sides           X              X           X           X
  are Parallel
Only One Set of
Opposite Sides                                                             X           X
  are Parallel
Opposite Sides                                                                        Non
 are Congruent                                                                      Parallel
                         X              X           X           X                   Sides are
                                                                                   Congruent
  All Sides are
   Congruent                                        X           X
Opposite Angles
 are Congruent           X              X           X           X
Adjacent Angles                                                                        X
       are                                                                         This is true
Supplementary            X              X           X           X          X        vertically
                                                                                     but not
                                                                                   horizontally
 All Angles are
   Congruent                            X                       X
 (Right Angles)
Base Angles are
   Congruent                                                                           X
  Diagonals are
   Congruent                            X                       X                      X
Diagonals Bisect
   Each Other            X              X           X           X
Diagonals Bisect
   the Angles                                       X           X
  Diagonals are
  Perpendicular                                     X           X
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Teacher’s Guide




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