Convince yourself of this theorem by making the following experiments in quad-1.seg.

  1. Check that the quadrilateral is really a parallelogram by choosing an edge and a vertex on the opposite edge to construct a parallel line. Since this parallel line includes the opposite edge, we have at least a trapezoid.

  2. Do the same for an edge adjacent to the original edge. Now the trapezoid is a parallelogram.

  3. Check that the diagonals bisect by chosing one diagonal and construct its midpoint. Note that it lies on the other diagonal.

  4. You can do the same for the other diagonal. Are you convinced now?

The above instructions might have been easier to follow if the vertices of the quadrilaterla had been labeled.

  1. Choose the four vertices and Edit>Unhide their labels.

  2. Edit the above instructions by inserting vertex labels.

Footnote: The word "choose" is a technical term for Kseg. To choose a point, place the cursor on it and left-click. To choose a line, place the cursor anwhere on the line, but not on a point on the line, and click. Hold the shift-key down to choose more than one object. Chosen objects turn red. If the wrong things turns red, unchoose it by clicking on the white space.

You can also choose new points located at the cursor by right-clicking. That is how how you’d start to construct a figure from scratch.

To "construct" is a also a technical term for Kseg. It means that a new geometrical thing, which depends on already present points and lines, is added to the figure. You choose exactly the objects that determine the desired construction, and click on the button in the menu.

For example, to draw the line through a point that is parallel to a given line (not through the point, of course), choose the point and the given line, and click on the button that looks like your construction. Note that this button doesn’t even appear until your choice. Note also, once chosen, Kseg offers to make other constructions based on a line and a point not on the line. For example, the perpendicular through the point to the line.