Constructions and Scale Drawing

Constructing triangles

Angles of elevation and depression

Perpendicular bisectors

Bisecting angles

Scale drawings of bearings

Prerequisite Knowledge

• know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
• draw given angles, and measure them in degrees (°)
• identify:
  • angles at a point and one whole turn total 360°
  • angles at a point on a straight line total 180°
  • other multiples of 90°
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles

Key Concepts

• You use different methods to draw triangles depending on what information you are given.
  • Side, Side, Side is constructed using a pair of compasses and ruler
  • Angle, Side, Angle is constructed using a protractor and ruler.
  • Side, Angle, Side is constructed using pair of compasses, protractor and ruler.
• The perpendicular bisector of a line is a line that divides the first line into two
  equal lengths and is at right angles to it.
• The angle of elevation is the angle between the horizontal line of sight and the object.  The angle of depression is the angle between the line looking straight ahead and the line looking down at the object.
• A bearing is a compass direction.  A three figured bearing is a clockwise angle measured from North.  North lines are parallel.
• The bisector of an angle is the line or line segment that divides the angle into two equal parts.

Working mathematically

Develop fluency

• Use language and properties precisely to analyse 2-D and 3-D shapes.

Reason mathematically

• Begin to reason deductively in geometry using geometrical constructions

Solve problems

• Begin to model situations mathematically and express the results using a range of formal mathematical representations.
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Geometry and measures

• Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
• Derive and 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); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line
• Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles,
• Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles
• Identify and construct congruent triangles