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Interactivity - Construct a parallelogram ABCD with vertices A, B and C   

Directions for interactivity

In the top right: Reset button to start over or Undo button to undo last step.

First draw sides \overline{AB} and \overline{BC}    How?

  • Select the line segment tool and click on A and then on B (they will glow).
    • You will get a line segment a joining A and B.
  • Click on B and then on C.
    • You will get a line segment b joining B and C.

Now pick any of the 3 ways below to draw a parallelogram. You will always get the point D(-3,4)!

One way to draw the parallelogram (based on definition that opposite sides are parallel).   How?

  • Select the parallel line tool and click on point A and then on line b.
    • You will get a line c passing through A and parallel to b=\overline{BC} .
  • Click on point C and then on line a.
    • You will get a line d passing through C and parallel to a=\overline{AB} .
  • Click on the intersection tool and then click on the intersection point of c and d.
    • You will get the point D at (-3,4).

Another way to draw the parallelogram (based on definition that opposite sides are the same length).   How?


 *Select the compass tool and click on center point A and then on B and on C.

  • You will get a circle c with center A and radius the length of b=\overline{BC} .
  • Click on point C and then on A and on B
    • You will get a circle d with center C and radius the length of a=\overline{AB} .
  • Click on the intersection tool and then click on the intersection point of c and d.
    • You will get the point D at (-3,4).

A third way to draw the parallelogram (based on definition that the diagonals bisect each other).   How?

  • (With the line segment tool still selected, draw the diagonal c=\overline{AC} .
  • Select the midpoint tool and click on c.
    • You will get the midpoint D of   b=\overline{AC} . Right-click on the label "D", select rename and type in E and click on OK.
  • Click on the line tool and click on B and then on E to get the line d.
  • Click on the circle-center-point tool and then click on E and then on B.
    • You will get a circle e with center E and radius the length of a=\overline{EB} . (It will pass through B.)
  • Click on the intersection tool and then click on the intersection point of line d and circle e.
    • You will get the point D at (-3,4).
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How to save interactivity
  • To save and then use the saved file, you will need to download and install GeoGebra
  • If there is a menubar, click on File -> Save.
  • If there is no menubar, double-click anywhere in the interactivity. A separate GeoGebra window will open (with menubar).


  Click on File -> Save.


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Page last modified on January 28, 2009, at 12:49 PM