Angle Geometry

Students learn how to discover various angle properties such as angles on a straight line, about a point, in a triangle and on parallel lines.  As learning progress they are challenged to construct polygons and solve problems involving their interior and exterior angles.  Angle properties is studied in Term 4, Year 9  of the Higher GCSE course and is prerequisite knowledge for circle theorems.


Angle Geometry Lessons
Revision Lessons

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 and 1/2 a turn (total 180°)
    • other multiples of 90°
  • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles;

Success Criteria

  • Understand and use alternate and corresponding angles on parallel lines;
  • Derive and use the sum of angles in a triangle (e.g. to deduce use the angle sum in any polygon, and to derive properties of regular polygons)
  • Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

Key Concepts

  • Rather than being told (or given) angle properties students should have the opportunity to discover and make sense of them practically.
  • Geometric problems can often be solved using various angle properties. Encourage students to look for and apply alternative properties.
  • Demonstrate how a polygon is made up from interior triangles when calculating their angles.
  • Bearings always go clockwise from North and have three digits. North lines are parallel.

Common Misconceptions

  • Students often forget the definition of properties associated to angles in parallel lines.
  • Exterior angles in a polygon have to travel in the same direction for the sum to be 360°.

Mr Mathematics Blog

Trigonometric Identities Sin, Cos and Tan

How to introduce the sin, cos and tan trigonometric identities.

Calculating a Reverse Percentage

How to teach calculating the original amount after a percentage change.

Comparing Datasets using the Mean and Range

The importance of the range when comparing comparing datasets.