Angles - points, lines and parallel lines

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

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?

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?