Constructing Triangles (Cambridge (CIE) IGCSE Maths)
Revision Note
Written by: Jamie Wood
Reviewed by: Dan Finlay
Constructing SSS Triangles
What are SSS Triangle constructions?
SSS just stands for side, side, side!
An SSS triangle construction is a triangle drawn accurately if you are told the lengths of its three sides and no other information
You will need:
a pencil
a ruler
a pair of compasses
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 givenThis 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 sidesBeing 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 sideBeing 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 questionWhen 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
Examiner Tips and Tricks
SSS triangle construction questions are usually worth 2 marks; one for having the sides accurate and the other for clearly showing the construction arcs on your diagram
To ensure you get that second mark
Make sure you are confident using a pair of compasses accurately
Do not erase the construction arcs from your diagram
Worked Example
Using a ruler and pair of compasses only, construct a triangle with sides 6 cm, 7 cm and 10 cm.
Do not erase your construction arcs.
Draw the 10 cm line as the horizontal base
In turn, place the point of the compasses at each end and draw an arc with radius 6 cm from one end, and another arc with radius 7 cm from the other end
The third vertex of the triangle is the point at which they intersect
Use your ruler to measure each side and check for accuracy
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