Angles inside

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Problem

Angles Inside printable sheet



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?