Angles - points, lines and parallel lines

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

Can you find triangles on a 9-point circle? Can you work out their angles?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

How did the the rotation robot make these patterns?