Constructions and Loci

Students learn how to construct angle and line bisectors using a pair of compasses.  Later, students apply this knowledge to solve problems involving loci about a point and line.  This unit takes place in   Year 9 Term 6.

Constructions and Scale Drawings Lessons

Prerequisite Knowledge

  • Identify and construct a radius, diameter, circumference, area, chord, tangent and arc.
  • Measure and begin to record lengths and heights
  • Identify acute and obtuse angles and compare and order angles up to two right angles by size

Success Criteria

  • Use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle);
  • Use these to construct given figures and solve loci problems;
  • Know that the perpendicular distance from a point to a line is the shortest distance to the line.

Key Concepts

  • It is important for students to sketch the diagram before attempting their construction. The sketch should be drawn freehand and contain all the necessary information.
  • Bisectors are used to half an angle as well as a length of a line segment.
  • Constructing a 60° angle using a pair of compasses is an essential skills throughout this topic as it goes on to equilateral triangles and reflex angles.

Common Misconceptions

  • Students often have difficulty constructing smooth arcs using a pair of compasses. Encourage them to try different techniques such as rotating the paper rather than the compasses.
  • It is important to leave in construction lines as these form the working out.


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