UCL Online STEP and AEA Preparation Sessions
Session 7: Geometrical Problems
Being able to use geometrical properties to deduce information about a figure is
important. Solving geometrical problems can also require


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good diagrams
experimenting by adding elements such as lines or circles to diagrams to
reveal relationships
using algebra alongside geometry where necessary
In this diagram what is the sum of the four
shaded angles?
This problem is reasonably straightforward
but in producing a solution it would be
important to be clear about which
geometric properties you are using at all
times.
Here is another example
Find the angle between a space diagonal of a cube and
one of its faces. It might not be immediately obvious that
some standard techniques from A level Mathematics will
enable this to be done relatively quickly.
Example problem
Show that the shortest distance from the point  ,   to the line y  mx  c has the value
m  c  
m2  1
.