Thinking mathematically

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Join pentagons together edge to edge. Will they form a ring?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?