Two Parallelograms, Common Vertex

Author:
Arthur Lee
In this exploration, you will make 2 parallelograms with 6 given points and one shared vertex to be found. Set up:
  • Adjust the 6 blue points to make 2 parallelograms with a fixed common vertex O.
  • The 2 quadrilaterals will be shaded only if they are parallelograms.
  • After making the parallelograms, hide all the segments and point O.
Explore:
  • Move the point P to any position so that it will make 2 parallelograms with all the 6 blue points.
  • The original point O is one possible position.
  • What other possible positions can you find?
  • How many possible positions can there be?
  • You may click the 'hint' so that an answer will be revealed when P is close enough.