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```					                                      Teacher’s Guide
Student Worksheet
Assignment 1

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.

 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
Assignment 2

   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
   Complete the Student Worksheet for assignment 2 and turn it in along with this page.

My File Name is _QUAD2 R Grunloh.gsp________________

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Teacher’s Guide
Student Worksheet
Assignment 2
Directions: Open three of your classmates files and determine the more specific names of their
File Name:              File Name:             File Name:

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.
 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
Student Worksheet
Assignment 3
   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.
 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
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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