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Angles Inside

Age 11 to 14 Challenge Level:
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?