Download The Aim of this lesson is to show you how to use a

Cabri Worksheet
Midpoints of a quadrilateral
South Hunsley School
Mathematics Department
The Aim of this lesson is to show you how to use a dynamic geometry
software package called Cabri Geometre. A dynamic geometry software
package allows you to do the sort of constructions you can do with a pencil,
ruler and compasses, but because it is ‘dynamic’, you can move parts of the
construction around to see what happens if things change.
Each section will guide you through a construction and then ask you some questions about
it. It is important that you always label any point that you draw. You may need to use the
‘Cabri Help Sheet’.
Construction
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Place 4 Points anywhere on the page. Label The Points A, B, C and D.
Draw Polygon ABCD. (Remember to click on A to finish).
Mark the Midpoint of side AB. Label this Point P.
Mark the Midpoints of sides BC, CD and AD.
Label these Points Q, R and S respectively.
Draw Polygon PQRS. (Remember to click on P to finish).
Mark Angles PQR and PSR. Measure Angles PQR and PSR.
Mark Angles QRS and SPQ. Measure Angles QRS and SPQ.
Your construction is now complete. You can move points A, B, C and D using
the Arrow tool.
Show your construction to your teacher and ask if you can print it. Now answer the
questions. You can write the answers on your printout.
1.
2.
3.
4.
What do you notice about the Angles?
What shape is PQRS?
Is this the same if you move points A, B, C and D?
On your construction, test if objects are parallel for side PQ and side RS.
Repeat this for sides QR and PS. Does this confirm your answer to question
2?
Fact Time:
 If you join the midpoints of the four sides of any quadrilateral the
shape produced is always a parallelogram.
 The opposite angles in a parallelogram are equal.
 The opposite sides of a parallelogram are parallel.
Can you make a ABCD rectangle? What shape does this make
PQRS?