Worked Example 1
Construct triangle XYZ with XY = 6 cm, YZ = 5 cm and ZX = 4 cm
Check firstCheck first: largest side is 6. The other two add to 4 + 5 = 9, and 9 is more than 6, so the triangle exists.
| Step | What you do |
|---|---|
| 1 | With a ruler, draw XY exactly 6 cm long. |
| 2 | Set the compass to 4 cm against the ruler. With X as centre, draw an arc above XY. |
| 3 | Set the compass to 5 cm. With Y as centre, draw an arc cutting the first one at Z. |
| 4 | Join XZ and YZ. Triangle XYZ is complete. |
Check at the endMeasure XZ and YZ with a ruler. They should read 4 cm and 5 cm. If one is out by more than a millimetre, your compass width slipped when you set it against the ruler.
Worked Example 2
Construct triangle PQR with PQ = 6 cm, angle P = 60° and PR = 5 cm
Identify the caseTwo sides, PQ and PR, and the angle P sits between them. This is SAS. Notice that both given sides start at P, which is what between means.
| Step | What you do |
|---|---|
| 1 | Draw PQ = 6 cm with a ruler. |
| 2 | At P, construct 60° with the compass: arc from P cutting PQ, then step the same radius round once. |
| 3 | Draw the arm from P through that mark, longer than 5 cm. |
| 4 | Set the compass to 5 cm. From P, cut the arm at R. |
| 5 | Join RQ. Triangle PQR is complete. |
A question worth askingHow long is RQ? You were never told, and you never measured it, yet it came out at a definite length. That is what it means for three pieces of information to fix a triangle: everything else follows whether you asked for it or not.