Angles - points, lines and parallel lines

problem

Spirostars

Age

16 to 18

Challenge level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
problem

Flight Path

Age

16 to 18

Challenge level

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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?
problem

Flower

Age

16 to 18

Challenge level

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.
problem

Right Angle Challenge

Age

5 to 7

Challenge level

How many right angles can you make using two sticks?
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

Sweeping Hands

Age

7 to 11

Challenge level

Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.
problem

Overlapping Squares

Age

7 to 11

Challenge level

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.
problem

The Numbers Give the Design

Age

7 to 11

Challenge level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
problem

Dotty Relationship

Age

7 to 11

Challenge level

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.