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.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

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?

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?