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?
Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
Why does this fold create an angle of sixty degrees?
Is it possible to find the angles in this rather special isosceles triangle?
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
