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Students learn how to construct triangles to scale using a pair of compasses and protractor. As learning progresses they construct angle and line bisectors using a pair of compasses. Finally, students apply this knowledge to solve problems involving loci about a point and line. This unit takes place in Year 10 Term 2.

**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.

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