Every construction below is written the way you should write it in an exam: what you are given, what you want, then numbered steps, then the check. Marks are given for the steps, not just the final picture.
Worked Example 1
Construct an angle of 90° using only a compass and a ruler
Think firstWhere does 90 sit? Radius steps give me 60 and 120. And 90 is exactly halfway between 60 and 120. So this is a bisection problem, not a new construction.
| Step | What you do | Why |
|---|---|---|
| 1 | Draw a ray OA. | This is the fixed arm. |
| 2 | With O as centre and any radius, draw an arc cutting OA at P. | This radius will now be used for everything. |
| 3 | With P as centre and the same radius, cut the arc at Q. | Angle QOP is 60°. |
| 4 | With Q as centre and the same radius, cut the arc at R. | Angle ROP is 120°. |
| 5 | With Q and R as centres and a radius more than half of QR, draw two arcs meeting at S. | This bisects the gap between 60 and 120. |
| 6 | Join OS. | Angle SOP = 60 + 30 = 90°. |
CheckMeasure angle SOP with a protractor. It should read 90°. If it reads 88 or 92, your compass width slipped between steps 3 and 4.
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