Geometry
Geometers’ Sketchpad Properties of Quadrilaterals
Name___________________________________
Open file in Class_Pickup folder: “Properties of quadrilaterals.GSP”
 There are 2 tabs at the bottom, “6.4 parallelograms” and “6.5 Trapezoids and kites”
 A higher accuracy decimal place may be required to recognize some of these patterns. To change the units preference,
go to Edit->Preferences. Changing Distance to “thousands” may help you see the patterns.
Discovery Activity 1: Investigating properties of special parallelograms….rhombus, rectangle, square
Part I. Create the parallelogram
1. Select tab “6.4 parallelograms”
2. Create a parallelogram ABCD using the segments AB and BC given in the diagram.
a. Construct a line through C parallel to AB
i.
Select AB and point C. “Construct->Parallel lines”
b. Construct a line through A parallel to BC.
i.
Select BC and point A. “Construct->Parallel lines”
c. Label the point of intersection of these 2 lines as D.
d. Hide the parallel lines
i.
Select the 2 parallel lines (make sure point D is not selected)
ii.
“Display->Hide Parallel Lines”
e. Construct AD and CD to complete the parallelogram ABCD
f. Construct the diagonals of parallelogram ABCD.
i.
Label the point of intersection as E.
Part II. Set up measurements to be used for the investigation.
M1: Angle measure at a single vertex (to be used for checking for rectangle): mABC
M2: Length of 2 adjacent sides (to be used for checking for rhombus): AB and BC
M3: Angle measure at the intersection of the diagonals:
mAEB
M4: Length of each diagonal AC and BD
M5: Angle measure of the two angles at a vertex created by the diagonal. mADE and mCDE
Part III. Investigate and make conjectures
1.Rectangles
a. Drag vertex B to make the parallelogram into a rectangle (look at M1). Why is only 1 angle measurement
sufficient to verify we have a rectangle? ________________________________________________________
b. Record your measurements for M4: AC =______________ BD =___________________________
c. Conjecture 1: The diagonals of a rectangle_______________________________________________________
2. Rhombus
a. Drag a vertex to make a rhombus (look at M2) Record your measurements for M3: mAEB =______________
and M5: mADE =___________ and mCDE =______________________
b. Conjecture 2: The diagonals of a rhombus____________________________________________________ and
__________________________________________________________________.
3. Square
a. Drag a vertex to make a square (look at M1 & M2). Record your measurements for M3: mAEB =__________,
M4: AC =_____________ BD =____________ M5: mADE =___________ and mCDE =____________
b. Conjecture 3: The diagonals of a square________________________________________________________
and
____________________________________________________________________________ and
_____________________________________________________________________________.
Part IV. Extension. Do you think the converses of your conjectures are true? Try manipulating the diagonals to verify
one of your conjectures and give your conclusion here.______________________________________________________
Discovery Activity 2: Investigating properties of kites and trapezoids
Using the current file “Properties of quadrilaterals.GSP”,
Part I. Create a Trapezoid
1. Select tab “6.5 Trapezoids”. Create a trapezoid ABCD using the segments AB and BC given in the diagram.
2. Construct a line through C, parallel to AB
a. Select AB and point C. “Construct->Parallel lines”
3. Construct a segment from A to a point on the parallel line.
a. Label the point D
4. Hide the parallel line used in the construction
a. Select the parallel line (make sure nothing else is selected)
b. “Display->hide Parallel line”
5. Construct CD to complete the trapezoid ABCD.
6. Construct the diagonals of the trapezoid.
Part II. Set up measurements for the investigation.
M6: Length of both legs of the trapezoid: BC and AD
M7: Measure each bottom base angle: mDAB , mABC , and
and measure of each top base angle : mBCD , m CDA
M8: Length of each diagonal AC and BD
Part III. Investigate and make conjectures for an isosceles trapezoid
1. Drag point D until you have an isosceles trapezoid. (use M6 to verify).
(Observe the changes in measurements M7 and M8 as you drag point D)
2. Record measurements for M7: Bottom base angles: mDAB = _______ and mABC =_______________
Top base angles:
mBCD = _______ and mCDA =______________
2. Record your measurements for M8: AC = ______________ and BD=____________________
3. Make a conjecture
Conjecture 1: The base angles of an isosceles trapezoid _________________________________
Conjecture 2: The diagonals of an isosceles trapezoid ___________________________________
Part IV. Extension: Create a new sketch and construct a kite (no parallel lines needed for this one).
Make a conjecture about the angles formed at the intersection of the diagonals of the kite.
_____________________________________________________________________________