Constructions

A post to clarify the requirements for the UK GCSE Mathematics specification.

  • You should make accurate drawings of triangles and other 2D shapes using a ruler and a protractor
  • make an accurate scale drawing from a sketch, diagram or description
  • construct a triangle
  • construct an equilateral triangle with a given side or given side length
  • use a straight edge and a pair of compasses to do standard constructions

For constructing triangles, have a look at these step by step instructions from BBC Bitesize.

BBC Bitesize – Constructing Triangles

The following demonstrations show how to use a straight edge and a pair of compasses to do standard constructions.

On Corbett Maths you will find clear demonstrations and also practice questions on constructions.
Look at this alphabetical list of contents, you will find several several items under Constructions. There are videos and also clearly worked answers to practice questions. Answers are all provided.

bisect-angle-math-open-ref

Use the standard ruler and compass constructions

Math Open Ref Instructions
Note that all these Math Open Reference demonstrations are available as a printable atep by step instruction sheet, see for example the guide to bisecting an angle.

The AQA specification also includes a note that Constructing a 60° angle is required. This is shown here by constructing an equilateral triangle.
 
​Students will be asked to use these constructions to construct given figures and solve loci problems. Students should also know that the perpendicular distance from a point to a line is the shortest distance to the line.
 
The constructions shown here are all from the excellent Math Open Reference by John Page. (There are many more constructions given on the site which are not a GCSE requirement). Another very useful source for demonstrations comes from BBC Bitesize on Loci and Constructions which gives step by step diagrams and instructions.BBC Bitesize Constructions
The BBC site also has clear examples of solving problems using constructions.
 

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