Angles in Parallel Lines and Polygons

Students discover the properties of interior, corresponding and alternate angles in parallel lines.  As learning progresses they are challenged to prove each property using algebraic and geometrical notation.  Later, students use interior and exterior angles of polygons to solve complex problems.

This topic takes place in  Term 1 of Year 8 and follows on from Basic Angle Properties which students learned in Year 7.

Angles in Parallel Lines and Polygons Lessons
Prerequisite Knowledge
  • Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
  • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  • Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon
Key Concepts
  • Alternate angles appear in ordinary and stretched out Z shapes and are equal.
  • Corresponding angles appear in F shapes.  The F shape can be reflected or rotated.  Corresponding angles are equal.
  • Interior angle appear in C shapes and have a sum of 180°.
  • Students should be able to prove each angle property using algebraic notation.
  • Students need to be able to combine multiple angle properties to solve a larger problem.
  • All the exterior angles of a polygon have a sum of 360°.
  • An interior and exterior angle lie along a straight line.  Therefore interior plus exterior angle equals 180°.
  • Students are often expected to combine multiple angle properties when calculating angles in polygons.
Working mathematically

Develop fluency

  • Use language and properties precisely to analyse 2-D shapes
  • Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

  • Make and test conjectures about patterns and relationships; look for proofs or counter-examples
  • Begin to reason deductively in geometry, including using geometrical constructions

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
Subject Content


  • Understand and use the relationship between parallel lines and alternate and corresponding angles
  • Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

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