Rhombus

This shape has been constructed so that when the vertices A, C and D are moved, it is always a rhombus.
Try moving the vertices, what changes? What stays the same?

Now draw the diagonals by selecting the segment tool and left-clicking on A and C and then B and D.
Select the point tool and put a point on the intersection point of the two diagonals.

Check that the diagonals bisect each other.
Measure the angle between DE and EC.
What do you notice about the angle DEC as the vertices are moved?

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Acknowledgements: http://www.lsp.open.ac.uk/geometry/

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