Angles - points, lines and parallel lines

problem
LOGO challenge 7 - more stars and squares

Age

11 to 16

Challenge level

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
problem
LOGO challenge 8 - rhombi

Age

7 to 16

Challenge level

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
problem
LOGO challenge 1 - star square

Age

7 to 16

Challenge level

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.
problem
Take the right angle

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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?
problem
Parallel universe

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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.
problem
Angle trisection

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
On time

Age

11 to 14

Challenge level

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?