Constructions and Scale Drawings

Angle, Side, Angle

Side, Side, Side

Side, Angle, Side

Constructing Bisectors

Locus about a Point and Line

Equidistant Paths

Constructing Loci

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 conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description
• 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.