Sheet № 161 · Foundation + Higher · AQA · Edexcel · OCR
Perpendicular Bisector and Angle Bisector –
Compass-and-ruler constructions are a classic GCSE Maths topic that appear on both Foundation and Higher papers across AQA, Edexcel, and OCR. You must be able to construct a perpendicular bisector of a line segment and an angle bisector accurately, leaving all construction arcs visible. This guide gives you the exact steps for each constr
§Key definitions
Question:
Construct the perpendicular bisector of a line segment AB that is 8 cm long.
Answer:
The perpendicular bisector passes through the midpoint of AB at 90°.
Q1 (Foundation):
Construct the perpendicular bisector of a line segment PQ of length 10 cm. Mark the midpoint M.
Q2 (Foundation):
Construct the bisector of an angle of 80°. Measure each half to verify.
Q3 (Higher):
Two points X and Y are 7 cm apart. Shade the region that is closer to X than to Y. Describe your method.
§Formulas to memorise
A perpendicular bisector passes through the midpoint of a segment at 90°
An angle bisector divides an angle into two equal halves
Any point on the perpendicular bisector of AB is equidistant from A and B
Open your compass — to more than half the length of the line segment.
Place the compass point on one end — of the line segment and draw arcs above and below the line.
Without changing the compass width — , place the point on the other end and draw arcs above and below, crossing the first pair of arcs.
Draw a straight line — through the two points where the arcs intersect. This is the perpendicular bisector.
Leave all construction arcs visible — the examiner needs to see them.
Place the compass point on the vertex — of the angle and draw an arc that crosses both arms of the angle.
Place the compass on one intersection point — and draw an arc between the two arms.
Worked example
Construct the perpendicular bisector of a line segment AB that is 8 cm long.
Working:
⚠ Common mistakes
- ✗Rubbing out construction arcs. The examiner awards marks for seeing the arcs. Never erase them.
- ✗Setting the compass too small. If the compass width is less than half the line segment, the arcs will not cross. Always use a width greater than half the length.
- ✗Moving the compass width between steps. The accuracy of the construction depends on keeping the compass width consistent within each set of arcs. If it slips, the result will be inaccurate.
✦ Exam tips
- →Use a sharp pencil for accuracy — thick lines lose precision and may cost marks.
- →Practise these constructions at home before the exam so the steps become automatic.
- →The examiner may check accuracy to within 1 mm and 1° — take your time.
- →Constructions are often part of loci questions, so mastering these two techniques is essential for the next step.
- →Always label the key points and lines in your construction.