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Investigating Quadrilateral Properties with Geometry Sketchpad
Teacher Notes:
Students construct each special quadrilateral in Geometer’s Sketchpad, then move it around
to investigate which properties each has. Fill in a table to show the different properties of all special
quadrilaterals.
Option 1: Students all do each quadrilateral, working in pairs. This would likely take 3 days or so
to do all 6 (or 7) quads.
Option 2: Students work in groups (e.g. 2 pairs at a table) to do different quadrilaterals and share
with class. This would likely take only one long-block, or two regular days.
On the following pages are:
 Graphic organizer to review/define the special quadrilaterals with teacher directed notes;
 Table to fill in / check off the properties of each special quadrilateral;
 Instructions for constructing each special quadrilateral in GSP;
Students will need basic skills using GSP to draw and measure. If necessary, complete
ca#01Skills and ca#01A first. These files are attached as pdf files. Students will explore the tools
and menu commands in Sketchpad, and also practice specific construction and measuring skills
through completing these two activities. This may add an extra day or less.
Alternately, you could pull out specific skills on these pages as needed and include them on
a separate sheet for reference as students need them.
The activity has a Part A, which includes instructions for constructing each special quadrilateral in
GSP. Instructions are very specific, with diagrams to go along. This along with having a partner
should minimize the amount of troubleshooting the teacher needs to do with students using GSP for
the first time.
Then there is a Part B, which explains and guides students in measuring their special quad to check
for properties, one at a time. This part is the same for every special quadrilateral. Again, the
instructions are pretty specific, but do not include how to measure in GSP. It is assumed students
have learned that skill. If not, instructions would need to be added.
Defining Special Quadrilaterals
Quadrilateral
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Kite
Definition
Diagram with markings
Opposite Sides
Opposite Angles

Sum of Consecutive
Angles  180
Diagonals

Diagonals

Diagonals Bisect each
other
Diagonals Bisect
Opposite Angles
Kite
Trapezoid
Square
Rhombus

Rectangle
In the chart below, place a 
in the box if you determine
that the quadrilateral listed
has that property. If not, leave
it blank.
Parallelogram
Quadrilateral Properties Chart
Properties of Parallelograms
Part A: Constructing the Parallelogram:
Follow the instructions below to construct a parallelogram and investigate its properties.
Remember, when told to Construct, you must use the menu command Construct. When told to
Draw, you may use the mouse drawing tool.
1. In the Edit menu, set the Preferences so that the precision of angle degree measurements is
units. Leave hundredths as the precision for all other measures.
2. Draw a horizontal segment. The endpoints should be labeled A
and B. (If not, change them).
3. Draw a point C floating above AB .
C
A
B
4. Draw AC .
C
5. Click on the line segment AB and the point C, making sure
nothing else is selected. Now choose Construct, Parallel Line
from the menu.
A
6. Click on the line segment AC and the point B, making sure
nothing else is selected. Now choose Construct, Parallel Line
from the menu.
7. Click on the two lines you just constructed and choose
Construct, Intersection from the menu. Label the point D.
C
A
8. Now, click on the two lines and choose Display, Hide Parallel
Lines. You should still see all points. Draw in segments CD
and BD .
9. Now, grab each vertex or side, one at a time, and move it
around using your mouse. The shape should stay a
parallelogram no matter how you move it.
B
D
B
C
A
Congratulations! You just constructed Parallelogram ABDC!
EXPLAIN WHY THESE INSTRUCTIONS WORKED TO MAKE A GUARANTEED
PARALLELOGRAM.
D
B
Properties of Rectangles
Part A: Constructing the Rectangle:
Follow the instructions below to construct a rectangle and investigate its properties. Remember,
when told to Construct, you must use the menu command Construct. When told to Draw, you may
use the mouse drawing tool.
1. In the Edit menu, set the Preferences so that the precision of angle degree measurements is
units. Leave hundredths as the precision for all other measures.
2. Draw a horizontal segment. The endpoints should be labeled A
and B. (If not, change them).
C
A
3. Click on the segment AB and also point A. Choose Construct,
Perpendicular Line from the menu.
4. Draw a point C on your perpendicular line, above AB .
B
C
5. Click on the line segment AB and the point C, making sure
nothing else is selected. Now choose Construct, Parallel Line
from the menu.
A
B
suur
6. Click on the line AC and the point B, making sure nothing else
is selected. Now choose Construct, Parallel Line from the menu.
7. Click on the two lines you just constructed and choose
Construct, Intersection from the menu. Label the point D.
8. Now, click on the three lines (not AB !) and choose Display,
Hide Lines. You should still see the points. Draw in segments
AC , CD , and BD .
9. Now, grab each vertex or side, one at a time, and move it
around using your mouse. The shape should stay a rectangle no
matter how you move it.
C
D
A
B
C
D
A
B
Congratulations! You just constructed Rectangle ABDC!
EXPLAIN WHY THESE INSTRUCTIONS WORKED TO MAKE A GUARANTEED
RECTANGLE.
Properties of Rhombuses
Part A: Constructing the Rhombus:
Follow the instructions below to construct a rhombus and investigate its properties. Remember,
when told to Construct, you must use the menu command Construct. When told to Draw, you may
use the mouse drawing tool.
1. In the Edit menu, set the Preferences so that the precision of angle degree measurements is
units. Leave hundredths as the precision for all other measures.
C
2. Draw a horizontal segment. The endpoints should be labeled A
and B. (If not, change them).
A
3. Click on the segment AB and also point A. Choose Construct,
Circle by Center + Radius from the menu.
B
4. Draw a point C on your circle, above AB . Draw in segment
AC .
C
5. Click on the line segment AB and the point C, making sure
nothing else is selected. Now choose Construct, Parallel Line
from the menu.
A
B
6. Click on the segment AC and the point B, making sure nothing
else is selected. Now choose Construct, Parallel Line from the
menu.
7. Click on the two lines you just constructed and choose
Construct, Intersection from the menu. Label the point D.
8. Now, click on the two lines and the circle and choose Display,
Hide Path Objects. You should still see AB , AC and point D.
Draw in segments CD and BD .
C
A
9. Now, grab each vertex or side, one at a time, and move it
around using your mouse. The shape should stay a rhombus no
matter how you move it.
Congratulations! You just constructed Rhombus ABDC!
EXPLAIN WHY THESE INSTRUCTIONS WORKED TO MAKE A GUARANTEED
RHOMBUS.
D
B
Properties of Squares
Part A: Constructing the Square:
Follow the instructions below to construct a square and investigate its properties. Remember, when
told to Construct, you must use the menu command Construct. When told to Draw, you may use
the mouse drawing tool.
1. In the Edit menu, set the Preferences so that the precision of angle degree measurements is
units. Leave hundredths as the precision for all other measures.
2. Draw a horizontal segment. The endpoints should be labeled A
and B. (If not, change them).
C
3. Double-click on point A. You should see it do a little dance.
A
B
4. Now click on segment AB and also point B. Choose Transform,
Rotate from the menu. Use 90 as the Angle. Re-label the new
point as C.
C
5. Click on the segment AB and the point C, making sure nothing
else is selected. Now choose Construct, Parallel Line from the
menu.
A
B
C
D
A
B
6. Click on the segment AC and the point B, making sure nothing
else is selected. Now choose Construct, Parallel Line from the
menu.
7. Click on the two lines you just constructed and choose
Construct, Intersection from the menu. Label the point D.
8. Now, click on the two lines and choose Display, Hide Parallel
Lines. You should still see the point D. Draw in segments CD
and BD .
9. Now, grab each vertex or side, one at a time, and move it
around using your mouse. The shape should stay a square no
matter how you move it.
C
D
A
B
Congratulations! You just constructed Square ABDC!
EXPLAIN WHY THESE INSTRUCTIONS WORKED TO MAKE A GUARANTEED SQUARE.
Properties of Trapezoids
Part A: Constructing the Trapezoid:
Follow the instructions below to construct a trapezoid and investigate its properties. Remember,
when told to Construct, you must use the menu command Construct. When told to Draw, you may
use the mouse drawing tool.
1. In the Edit menu, set the Preferences so that the precision of angle degree measurements is
units. Leave hundredths as the precision for all other measures.
2. Draw a horizontal segment. The endpoints should be labeled A
and B. (If not, change them).
3. Draw a point C floating above AB .
C
A
B
4. Draw AC .
5. Click on the line segment AB and the point C, making sure
nothing else is selected. Now choose Construct, Parallel Line
from the menu.
C
A
6. Draw a point on the line you just constructed and label it D.
7. Now, click on the line only and choose Display, Hide Parallel
Line. You should still see point D. Draw in segments CD and
BD .
B
C
D
B
A
C
8. Now, grab each vertex or side, one at a time, and move it
around using your mouse. The shape should stay a trapezoid no
matter how you move it.
A
Congratulations! You just constructed Trapezoid ABDC!
EXPLAIN WHY THESE INSTRUCTIONS WORKED TO MAKE A GUARANTEED
TRAPEZOID.
D
B
Properties of Kites
Part A: Constructing the Kite:
Follow the instructions below to construct a kite and investigate its properties. Remember, when
told to Construct, you must use the menu command Construct. When told to Draw, you may use
the mouse drawing tool.
1. In the Edit menu, set the Preferences so that the precision of angle degree measurements is
units. Leave hundredths as the precision for all other measures.
D
2. Draw a horizontal segment. The endpoints should be labeled A
and B. (If not, change them).
3. Draw another segment with endpoint B. Re-label the other
endpoint D.
B
A
4. Click on the segment AB and also point A. Choose Construct,
Circle by Center + Radius from the menu.
D
5. Now click on the segment BD and also point D. Choose
Construct, Circle by Center + Radius from the menu.
B
A
6. Use the point tool to draw a point at the intersection of the two
circles you just created (make sure both circles turn red!). Label
this point C.
D
C
7. Draw in segments CD and AC .
A
B
8. Now, click on the two circles and choose Display, Hide Circles.
9. Grab each vertex or side, one at a time, and move it around
using your mouse. The shape should stay a kite no matter how
you move it.
Congratulations! You just constructed Kite ABDC!
D
C
A
B
EXPLAIN WHY THESE INSTRUCTIONS WORKED TO MAKE A GUARANTEED KITE.
Part B: Investigating Properties
1.
Opposite Sides  :
Measure the lengths of all 4 sides. Place the measurements of the opposite sides next to each
other. Is this property true? Grab a vertex of your quadrilateral and move it around. If the
measures of the opposite sides stay the same no matter what, then check off that box in your
table.
2.
Opposite Angles  :
Measure all 4 angles. Place the measurements of the opposite angles next to each other. Is this
property true? Grab a vertex of your quadrilateral and move it around. If the measures of the
opposite angles stay the same no matter what, then check off that box in your table.
3.
Consecutive Angles sum to 180 : Add the measures of consecutive angles. Is this property
true? Move around the quadrilateral to verify your conclusion. Check your table as appropriate.
4.
Diagonals  :
Draw in the diagonals of your quadrilateral. Measure their lengths. Determine and test whether
this property is true. Check the box in the table if appropriate.
5.
Diagonals  :
Click on the 2 diagonals and choose Construct, Intersection from the menu. Now, measure the
angle where the 2 diagonals intersect. Is this property true? Move around the quadrilateral to
verify your conclusion. Fill in the table as appropriate.
6.
Diagonals Bisect each other:
For each diagonal, measure the distances from each endpoint to their intersection. To do this,
click on one endpoint and the intersection point, and choose Measure, Distance from the menu.
(Note: You can’t use Measure, Length here because it will measure the whole diagonal
segment.) Use these measures to determine whether each diagonal has bisected the other,
cutting it into two equal pieces. Fill in your chart as appropriate.
7.
Diagonals Bisect Opposite Angles:
Now, at each vertex of your quadrilateral, measure the two adjacent angles created by the
diagonal. Is this property true? Repeat for each vertex. Remember to verify your findings by
moving around your quadrilateral. Fill in your chart as appropriate.