GEO018 · Geometry basics · Classes 6–9
Geometric constructions
A geometric construction uses only a compass and straightedge. To bisect AB: draw equal arcs (radius more than half AB) from A and B; the line through the two crossings is the perpendicular bisector.
⌒⌒Geometric constructions
📐 Formula
arcs of radius r > AB/2 from A and B
✏️ Worked example
AB = 6 cm: arcs of radius 4.2 cm meet above and below; joining them cuts AB at its midpoint M, 3 cm from A, at 90°.
🌍 Where it is used
Drawing accurate plans and designs without a protractor.
❓ Quick check
The perpendicular bisector of AB passes through…
🏋️ Practice
EasyWhy must the arc radius be more than half AB?
Answer: Otherwise the arcs do not meet
MediumAB = 9 cm. Distance from A to M?
Answer: 4.5 cm
ChallengeEvery point on the bisector is equally far from…?
Answer: A and B