Angles in Parallel Lines and Polygons

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

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

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.

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.

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