MathematicsExam code: 0580

Bearings, Constructions and Scale Drawings

Geometry

PractiseFlashcards

Three sides, ruler and compasses

  • The one construction required is a triangle from its three side lengths, using a ruler and compasses only
  • Work through it in the same order every time
    • Draw the longest side as a horizontal base, measured exactly, and write its length underneath
    • Set the compasses to the second side's length, rest the sharp point at one end of the base, and sweep an arc above it
    • Reset them to the third side's length, rest the point at the opposite end, and sweep a second arc across the first
    • Join both ends of the base to wherever those two arcs meet, using a ruler
An SSS construction: the longest side ruled as a horizontal base with a cross at each end, an arc swept from each end at the length of one of the other two sides, and the two remaining sides ruled from the base to where the arcs cross, with a note that the construction arcs must be left on the page
Source: Constructing SSS Triangles by Save My Exams
  • Measure the two new sides to check them against the question before labelling
A finished construction of a triangle with sides 10 cm, 7 cm and 6 cm: the 10 cm base ruled first, the two arcs still showing where they cross above it, and the 7 cm and 6 cm sides ruled up to that crossing point
Source: Constructing SSS Triangles by Save My Exams
  • Leave the arcs on the page. They are the evidence that compasses were used, and a mark depends on them
  • Where the triangle is named, such as triangle ABC, label each corner with the right letter
  • The same method builds other shapes, since a rhombus is two triangles sharing a side

Exam tip

Swing each arc from the end its length names

When the base AB is drawn for you, swing each arc from the end its length shares with the base: the compasses set to AC go on A, and those set to BC go on B. A triangle with the two lengths swapped loses at least one mark in the schemes, even with correct arcs, and so does a point located from two distances the wrong way round. Check each new side against its name.

Worked example

An SSS construction

Using a ruler and a pair of compasses only, construct a triangle with sides of 5 cm, 8 cm and 9 cm.

Solution:

  • Draw the longest side, 9 cm, as a horizontal base and label it
  • Set the compasses to 8 cm, rest them at the left end of the base and sweep an arc above it
  • Reset to 5 cm, rest them at the right end and sweep a second arc across the first
  • Rule a line from each end of the base to wherever the arcs meet
  • Measure the two lines to confirm they are 8 cm and 5 cm, then label them
  • Leave both arcs visible: the answer is the ruled triangle with both construction arcs showing
  • The three lengths do form a triangle, since the two shorter sides together, 5 + 8 = 13 cm, exceed the longest side of 9 cm
The finished construction: a 9 cm horizontal base, a side of 8 cm ruled from its left end and a side of 5 cm from its right end, with the two short construction arcs still showing where they cross at the top corner

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