Constructing SSS Triangles
What are SSS Triangle constructions?
- SSS just stands for side, side, side!
- In mathematics a construction is an accurate drawing that normally uses equipment such as a ruler, protractor and/or a set of compasses
- An SSS triangle construction is a triangle drawn accurately if you are told the length of its three sides and no other information
- This is harder to do than you might initially think, especially without the correct equipment
How do I construct an SSS triangle?
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If you are given all three sides of a triangle, you will need a pencil, a ruler and a pair of compasses
- 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, measure it carefully with your ruler
- Write its length (with units) just underneath
- STEP 2
- Using your ruler to measure, 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
- STEP 3
- Using your ruler to measure again, 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 itĀ 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 overĀ
- 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
- It is important that you 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
Exam Tip
- 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 fully equipped with a good set of compasses that you are confident using when you go into the exam room
- 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.
Leave in your construction arcs.
Draw the 10 cm line as the horizontal base.
Place the point of the compasses at each end and draw an arc with radius 6 cm from one end and another 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.
