Angles - points, lines and parallel lines

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Weekly Problem 16 - 2007
Can you figure out how far the robot has travelled by the time it is first facing due East?

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

Which hexagons tessellate?

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

Construct this design using only compasses

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?