To construct a triangle, draw the one side you know the full length of first, then use compasses (for a given side length) or a protractor (for a given angle) to fix the third vertex from the two ends of that line. To construct a quadrilateral, split it into two triangles with one diagonal and construct each triangle in turn. Leave every compass arc and ruled line visible: in the O-Level exam, the arcs are your proof of method and marks are lost if they are erased.
Most marks lost on construction questions have nothing to do with geometry knowledge. They come from rubbing out the compass arcs after finding the answer, setting the compass radius to the wrong length, or drawing the known side in the wrong place on the page so the rest of the shape runs off the paper. The examiner is checking your method, shown as visible arcs, not just the final outline.
The fix is a fixed order of operations: always draw the fully known side first, always fix vertices using arcs or angle lines from that side, and never erase construction marks. The same order works for every triangle and extends directly to quadrilaterals.
Step 1
Draw the one fully known side with a ruler
Step 2
From each end, swing an arc (given length) or draw a ray (given angle)
Step 3
Where the two arcs or lines meet is the third vertex
Step 4
Join the vertices with straight ruled lines, keep all arcs visible
O-Level questions give you exactly enough information to fix a unique triangle, in one of three combinations: three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA). These are the same combinations that appear in the congruence tests, and for the same reason: each one pins down exactly one triangle. Each combination uses the same compasses-and-ruler order but a different tool at step 2.
Construct triangle ABC with AB = 7 cm, BC = 5 cm and AC = 6 cm.
Solution
AB = 7 cm with a ruler and label both ends.AC). Place the point on A and swing an arc above the line.BC). Place the point on B and swing a second arc that crosses the first.C.A to C and B to C with a ruler. Leave both arcs visible: they are the evidence that AC = 6 cm and BC = 5 cm were measured, not guessed.Quick check: measure the completed AC and BC with your ruler. They should read 6 cm and 5 cm. If either is off by more than about a millimetre, a compass setting slipped while you were drawing and you should redo that arc.
Construct triangle PQR with PQ = 8 cm, angle QPR = 50°, and PR = 6 cm.
Solution
PQ = 8 cm with a ruler and label both ends.P, use a protractor to measure and mark an angle of 50° from PQ. Draw a faint ray from P through that mark.P and swing an arc that crosses the ray you just drew.R.Q to R with a ruler to complete the triangle.The step students get wrong
Reading the wrong scale on the protractor. A 50° angle and its supplement 130° sit on the two scales printed on most protractors, and it is very easy to read the outer scale when you meant the inner one. Always sanity-check: does the angle you have drawn look roughly like 50° next to a right angle, or does it look closer to 130°? If it looks wrong, it probably is.
Construct quadrilateral ABCD with AB = 6 cm, BC = 5 cm, CD = 4 cm, AD = 5.5 cm, and diagonal AC = 7 cm. Knowing which of the eight quadrilaterals you are drawing, from the property tables in triangles, quadrilaterals and symmetry, is a useful check that your finished shape looks right before you measure anything.
Solution
AC splits the quadrilateral into two triangles: ABC and ACD. Construct each one using the SSS method from worked example 1.AC = 7 cm first, since it is shared by both triangles and appears in both sets of given lengths.ABC: from A, swing an arc of radius 6 cm (AB). From C, swing an arc of radius 5 cm (BC). Label the crossing point B, on one side of AC.ACD: from A, swing an arc of radius 5.5 cm (AD). From C, swing an arc of radius 4 cm (CD). Label the crossing point D, on the opposite side of AC from B.A to B, B to C, C to D, and D to A with a ruler. Leave the diagonal AC and all four arcs visible.The step students get wrong
Placing B and D on the same side of the shared diagonal AC. That produces two overlapping triangles rather than a four-sided quadrilateral. Before joining any lines, check that your two crossing points sit on opposite sides of AC, so the final shape has four distinct vertices going around in order.
Once a triangle or quadrilateral is constructed accurately, many follow-on questions ask you to measure an angle or a length from your diagram, mark a point that is a fixed distance from a vertex, or shade a region bounded by two conditions. A common pairing is to construct the shape, then read off the bearing of one vertex from another with a protractor. See loci problems for how those regions are found once your shape is drawn. These questions depend entirely on the accuracy of the original construction, so a slipped compass setting early on can cost marks on several later parts.
Exam tip: read the whole question before you start constructing. If a later part asks you to mark the locus of points equidistant from two vertices, or to bisect one of the angles using the perpendicular and angle bisector constructions, plan enough space on the page for a large, undistorted diagram from the first line you draw.
Which side should I draw first?
Always draw the one side whose full length you are given directly, not a side you would have to calculate. In a quadrilateral built from two triangles, draw the shared diagonal first, since it appears in the given lengths for both triangles.
Do I need to erase the compass arcs once I have found the answer?
No. Leaving the arcs visible is required. The arcs are the visible proof that you constructed the shape with compasses rather than estimating it by eye, and examiners specifically look for them when awarding method marks.
What if the compasses cannot reach the width I need?
Most school compasses open to about 15 to 20 cm, which comfortably covers O-Level construction lengths. If a required radius is close to the maximum, draw your known side nearer one edge of the page so the arc has room to swing without running off the paper.
How is this different from constructing a perpendicular or angle bisector?
A perpendicular bisector or angle bisector construction fixes a line, not a full shape, and always uses two equal-radius arcs from a pair of points. Constructing a triangle fixes a vertex using arcs of two different given radii, or one radius and one angle. The compass technique overlaps, but the goal is different.
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Mr. Gan works with students who want a method that survives exam pressure, not just a diagram that looks right at home.
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