Constructing Triangles (Edexcel GCSE Maths)

Constructing Triangles

What are triangle constructions?

• A triangle construction is an accurate drawing that usually uses:

  • a sharp pencil

  • a ruler

  • a protractor

  • and/or a pair of compasses

• You will be given information about the size of some of the angles and/or sides of a triangle

• Depending on the type of triangle, you will need to follow a specific method and you may need different equipment

• The types of triangle you may be asked to construct include: 

  • SSS - you are given the lengths of all three sides

  • SAS - you are given the lengths of two sides and the angle in between them

  • ASA - you are given the size of two angles and the length of the side in between them

How do I construct an SSS triangle?

• STEP 1
  Use a ruler to draw the longest side as the horizontal base near the bottom of the space you have been given

  • This needs to be accurate

  • Write its length (with units) just underneath

• STEP 2
  Open your compasses so that the length from the compass point to the tip of your pencil is exactly the length of one of the remaining sides

  • Being extra careful not to change the length, put the compass point on one end of the horizontal line you have drawn and draw an arc above the horizontal line

  • You can draw a full circle rather than an arc if you prefer

• STEP 3
  Open your compasses so that the length from the compass point to the tip of your pencil is exactly the length of the third side

  • Being extra careful not to change the length, put the compass point on the other end of the horizontal line and draw another arc, making sure that it crosses the first arc

• STEP 4

  Use your ruler to draw straight lines from each end of the horizontal line to the point where the arcs cross

• STEP 5
  Use your ruler to check that the two new lines are exactly equal to the lengths given in the question

  • When you are confident that they are accurate, label the lines with their lengths and units

• Do not rub out your arcs as the examiner will use these to check your work

• Sometimes the instructions will include a triangle name such as triangle ABC

  • Make sure you label each vertex with the correct letters

How do I construct an SAS triangle?

• STEP 1
  Use a ruler to draw the longest given side as the horizontal base

  • This needs to be accurate, measure it carefully with your ruler

  • Write its length (with units) just underneath

• STEP 2
  Measure the angle from the end of the line

  • Place the centre point of the protractor on one end of the side that you have just drawn, measure the given angle, and make a mark to indicate where it is

  • Use a ruler to draw a straight line from where you placed the protractor, through the mark, and extend it further

• STEP 3
  Draw the second straight line

  • Measure along the line you have just drawn in STEP 2 from the end where it connects to the first horizontal line

  • Make a mark on the line when you have measured the length of the second given side

• STEP 4

  Use your ruler to draw a straight line from other end of the first horizontal line to the mark you have just made on the second line

• STEP 5
  Use your protractor and ruler to check that the measured angle and sides are exactly equal to the sizes given in the question

  • When you are confident that they are accurate, label the sides and the angle

• It is important that you do not rub out your construction lines as the examiner will use these to check your work

How do I construct an ASA triangle?

• STEP 1
  Use a ruler to draw the given side as the horizontal base

  • This needs to be accurate, measure it carefully with your ruler

  • Write its length (with units) just underneath

• STEP 2
  Measure one angle from one of the ends of the line 

  • Place the centre point of the protractor on one end of the side that you have just drawn, measure the given angle from the side and make a mark to indicate where it is

  • Draw a straight line from where you placed the protractor, through the mark and extend it further

• STEP 3
  Measure the second angle from the other end of the line

  • Repeat STEP 2 for the second angle, but from the other end of the horizontal line

  • This line should cross the line you drew in STEP 2, if it doesn't, extend both lines further so that they do intersect

• STEP 4
  Use your protractor to check that the two measured angles are exactly equal to the sizes given in the question

  • When you are confident that they are accurate, label the angles

• It is important that you do not rub out your construction lines as the examiner will use these to check your work