01 — Explanation
How do I accurately measure and draw a given angle?
Line up the centre point (crosshair) of your protractor exactly on the vertex of the angle, with the base line of the protractor running along one arm of the angle. Read off the scale that starts at on that arm. Always use a sharp pencil and a ruler for any straight edge — a blunt pencil can introduce enough line-width error to shift a reading by a degree or more.
02 — Explanation
How do I construct a triangle when I'm only given the three side lengths?
Using only a ruler and a pair of compasses (no protractor):
- Draw one side as a straight line at its correct length using the ruler — this is your base.
- Open the compasses to the length of the second side. Put the point on one end of the base and draw an arc above it.
- Open the compasses to the length of the third side. Put the point on the other end of the base and draw a second arc crossing the first.
- The point where the two arcs cross is the third vertex. Join it to both ends of the base.
03 — Explanation
Why does this "two arcs" method actually work?
Each arc represents every possible position a point could be from one end of the base, at the fixed distance of that side length. The correct third vertex must be exactly the given distance from both ends of the base simultaneously — so it has to lie on both arcs at once, which means it must be at their point of intersection. This is exactly why the construction is guaranteed accurate provided the arcs are drawn carefully, without needing to measure any angles at all.
04 — Explanation
Do I need to show my construction arcs?
Yes — construction arcs must be shown on the diagram. An examiner cannot award full marks for a "correct-looking" triangle with no visible compass arcs, since the arcs are the evidence of a valid construction method rather than a guess.
05 — Explanation
How can I construct a shape like a rhombus using this method?
A rhombus can be built from two congruent triangles sharing a common side (the rhombus's diagonal): construct one triangle from three known side lengths, then construct the mirror-image triangle on the other side of the shared edge using the same arc method.
06 — Explanation
How do nets connect to volume and surface area?
A net is the "unfolded" flat version of a 3D solid. Once a solid is unfolded into a net, you can measure or calculate each flat face separately: summing the areas of all faces in the net gives the solid's total surface area, and using the dimensions shown on the net (e.g. base and height of a cross-section) lets you calculate its volume.
Exam tip
Leave your compass arcs slightly long and visible rather than erasing them — Cambridge mark schemes specifically check for the arcs as proof of method, even when the final triangle itself is drawn correctly.
07 — Worked example
Worked example
Construct a triangle with sides , and using only a ruler and compasses.
- Draw the base: a straight line segment of , labelled to .
- Set compasses to , point on , draw an arc above the line.
- Set compasses to , point on , draw an arc crossing the first.
- Label the intersection point . Join and with a ruler.
- Leave all three arcs visible as evidence of the construction.