Revision notes
Construct perpendicular bisectors, perpendiculars and triangles with a ruler and compasses — and know why they work.
Two families share a plot and want the boundary exactly halfway, at right angles to the road. A surveyor can find it with pegs and a rope — the same way you do it with a pair of compasses.
Open the compasses to more than half of AB. With the point on A, draw arcs above and below AB.
Keep the same radius. With the point on B, draw arcs that cut the first two at P and Q. Join P and Q.
PQ cuts AB in half at 90°. P and Q are each the same distance from A and B, and so is every point on PQ.
🔑 Key idea: Every point on the perpendicular bisector of AB is the same distance from A and B.
With the compass point on P, draw an arc that cuts the line at A and B.
From A and then from B (same radius), draw arcs on the other side of the line that cross at Q. Join P to Q.
PQ meets the line at 90°, and this gives the shortest distance from P to the line.
🔑 Key idea: Arcs from P, then from A and B, give a line through P at right angles to the line.
Draw the longest side as the base, AB. Open the compasses to the second length and draw an arc from A; then to the third length and draw an arc from B. Where the arcs cross is C.
This only works if the two shorter sides together are longer than the longest side. With 3 cm, 4 cm and 8 cm, 3 + 4 = 7 < 8, so the arcs never meet.
🔑 Key idea: Two shorter sides added must be longer than the longest side.
AB = 5 cm. Point C lies on the perpendicular bisector of AB, and CA = 6 cm. How long is CB?
Step 1: Equal distances
CB = CA = 6 cm
Why? That is the special property of the perpendicular bisector.
Answer: 6 cm
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.