Bisectors and constructions

Objective. Construct perpendicular and angle bisectors accurately.

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2. Worked example
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Learn: the key idea

Bisectors and constructions use only a compass and straight edge to divide a line segment or angle exactly in half, with arcs marking equal distances to guarantee accuracy. A perpendicular bisector crosses a line at 90° through its midpoint, found by drawing equal-radius arcs from each end that intersect above and below the line. An angle bisector splits an angle into two equal parts, found by drawing an arc across both arms, then equal arcs from those points to find the bisecting line. Always keep the compass width fixed between arcs on the same construction step.

Worked example

Describe the steps to construct the perpendicular bisector of a line segment AB.

1 $Open compasses to more than half the length of AB$
2 $Draw an arc above and below AB from point A$
3 $Keeping the same width, draw arcs from point B crossing the first arcs$
4 $Join the two arc intersection points to form the perpendicular bisector$

Answer: Draw equal arcs from A and B and join their intersections

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Common mistake. Pupils often change the compass width between drawing arcs from each end of a line, producing an inaccurate bisector that doesn't cross at the true midpoint. Always keep the same compass radius for both arcs in one construction step.

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