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Published July 15, 2026

Accurate Drawings and Constructions

Billie Geena Hyde
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Accurate Drawings and Constructions

Geometric constructions use only a ruler and compasses to draw lines, angles, and shapes with perfect accuracy. This foundational skill is essential for understanding geometry, solving loci problems, and is a key part of your GCSE Maths exam.

The Four Key Constructions to Master

1. Perpendicular Bisector

Cuts a line segment exactly in half at 90°. Used to find the midpoint or the locus of points equidistant from two points.

Construction of a perpendicular bisector. A horizontal line has two compass arcs drawn from each end that intersect above and below the line. A blue vertical line through the intersection points is the perpendicular bisector. A red square marks the 90-degree angle. A horizontal green line segment. Two grey arcs, one from each endpoint of the line, cross above and below the midpoint. A blue vertical line passes through both crossing points, bisecting the original line at right angles.

2. Perpendicular from a Point to a Line

Creates a line perpendicular to an existing line passing through a specific point above it. Used to find the shortest distance from a point to a line.

Construction of a perpendicular from a point to a line. A horizontal line is shown with a point above it. A large compass arc from the point marks two intersections on the line. A smaller arc from below the line marks another intersection. A blue line from the point to the line is the perpendicular, with a right-angle marker where they meet. A horizontal green line with a red dot representing the point above it. Grey arcs show the compass construction steps. A blue vertical line descends from the point to meet the base line at a right angle marked by a small red square.

3. Angle Bisector

Splits an angle into two equal halves. Used to find the locus of points equidistant from two intersecting lines.

Construction of an angle bisector. Two rays extend from a vertex at the top. Compass arcs mark equal distances on each ray and then from those marks. A blue line from the vertex through the final arc intersection bisects the angle. Two green lines meet at a vertex at the top of the diagram, forming an angle. Grey arcs show the compass construction. A blue line descends from the vertex to bisect the angle exactly.

4. Constructing a 60° Angle

Uses the properties of an equilateral triangle (all angles 60°) to create a perfect 60° angle without a protractor.

Construction of a 60-degree angle. A base line is drawn. Two compass arcs of equal radius — one from each end of a marked segment — intersect above the line. A blue ray from the start point to the intersection makes a 60-degree angle with the base, marked with a small red arc. A horizontal green base line. Two grey arcs cross above the line at equal distances, marking the apex of an equilateral triangle. A blue line rises from the left end of the segment to the arc intersection, forming a 60-degree angle marked by a small red arc. 60°

Tutor Insights

🤔 Common Misunderstandings

  • Rubbing out construction arcs. Students often erase them, thinking they look messy. The arcs are your method and must remain visible — removing them costs marks.
  • Incorrect compass width. For a perpendicular bisector, the compass must open to more than half the line length. For a 60° angle, the compass radius must stay constant between arcs.

📝 Common Exam Mistakes

  • Using a protractor or ruler to measure. This scores zero marks on a construction question — the method must use only ruler and compasses.
  • Inaccurate drawings. A blunt pencil, wobbly compass, or damaged ruler can push answers outside the allowed tolerance.
  • Not labelling points or regions when the question asks for them.

Practice Questions

  1. Draw a line segment $AB$ that is 8 cm long. Construct its perpendicular bisector.
  2. Draw an angle of approximately 70°. Construct the line that bisects this angle.
  3. Construct an angle of 60°.
Show Answers

Your constructions should resemble the diagrams in the section above. The most important check is that all of your construction arcs are still visible on the finished drawing — these are your working and examiners will look for them.

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