Home → Curriculum Hub → Maths Lessons → Schemes of Work → Two-Year IGCSE Foundation → Constructions
Students can draw a length with a ruler and an angle with a protractor. This unit uses those tools, with a pair of compasses, to construct a triangle from three pieces of information and to bisect an angle. Side, side, side comes first, then angle, side, angle, then side, angle, side. The angle bisector comes last, once an arc is a familiar mark. The arcs stay on the page. They are the evidence of the construction.
Three sides need only compasses and a straight edge, so that method comes before a protractor is added. Angle, side, angle then fixes which angle sits at which end of the given side. Side, angle, side follows, because the given angle has to be the one between the two sides. Bisecting the 60° angle in an equilateral triangle gives 30°. Bisecting a right angle gives 45°. The perpendicular bisector of a line segment is not one of these four lessons.
By the end of this unit students will be able to:
Students should be secure with the following before beginning this unit.
Draw the base with a ruler. From each end, draw an arc whose radius is one of the other given sides. The arcs meet at the third vertex. If they do not meet, those three lengths cannot make a triangle. Two meeting points, one each side of the base, give congruent triangles. Leave both arcs.
For angle, side, angle, the given side is included between the two angles. Draw that side, then use the protractor at each end for the angle named at that end. The two rays meet at the third vertex. Drawing both angles at the same end builds a different triangle.
For side, angle, side, the given angle is the included angle. Draw one side, construct that angle at the correct end, and mark the second length along the new arm. Joining the ends completes the triangle. Two sides and a non-included angle are not this construction.
From the vertex, one arc cuts both arms. From those two points, two arcs of equal radius meet. The bisector is the line from the vertex through that meeting point. Every point on it is the same perpendicular distance from the two arms. Bisecting 60° gives 30°. Bisecting 90° gives 45°.
| Misconception | Teaching focus |
|---|---|
| Rubbing out the arcs once the triangle is drawn. | The arcs are the method, not rough working. A finished construction still shows them. |
| Swapping the two radii in a side, side, side construction, so the sides do not match the labels. | Write the length next to the compass before drawing each arc, and check it against the vertex it starts from. |
| Drawing both angles at the same end of the given side. | Label each end with its angle before the protractor is used. One angle, one vertex. |
| Treating two sides and a non-included angle as side, angle, side. | The given angle must sit between the two given sides. If it does not, it is a different set of information. |
| Using different radii for the second pair of arcs, so their meeting point is not on the bisector. | Keep the compass opening fixed for both of those arcs. Equal radii are what make the meeting point equidistant from the arms. |
Every lesson in this unit is already built. A Mr Mathematics membership gives you the presentation, worksheet, question generator and video tutorial for all four lessons, alongside the full Key Stage 3, GCSE, IGCSE and A-Level libraries.
A school membership covers every teacher in your department, so the whole scheme of work is resourced from one subscription.
Students learn how to construct triangles using a pair of compasses.
As learning progresses, they construct more complex shapes using the same techniques.
Students learn how to construct triangles using a protractor and straight edge.
Later, they construct polygons using the same techniques as learning progresses.
Students learn how to construct triangles when given SAS.
As learning progresses, they construct more complex shapes using the same techniques.
Students learn how to construct angle bisectors using a pair of compasses and a straight edge.
Later, students use equilateral triangles to construct 30° and 45° angles as learning progresses.
Additional practice constructing angle and perpendicular bisectors.
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