Angles in Parallel Lines and Polygons

Scheme of work: Key Stage 3: Year 8: Term 1: Angles in Parallel Lines and Polygons

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 angles 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

  • Shape
    • 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

Angles in Parallel Lines and Polygons Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

How to teach problem solving with angles in polygons through scaffolding.

Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.