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Draw a rectangle and choose a point inside. Join your point to two adjacent corners, and measure the angles as shown in the GeoGebra applet below.
Try a few examples. What do you notice?
Alison made a conjecture: "The green angle and blue angle add together to give the red angle."
Do your examples support Alison's conjecture?
Can you prove Alison's conjecture?
Can you prove it in more than one way?
What happens if you start with a parallelogram?
Or a trapezium?
What if the point goes outside the rectangle?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.