The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

How would you move the bands on the pegboard to alter these shapes?

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

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

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?

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

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Can you find all the different triangles on these peg boards, and find their angles?

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

Turn through bigger angles and draw stars with Logo.

Are these statements always true, sometimes true or never true?

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.