# 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.

#### The Sum to Infinity of Geometric Series – A-Level Maths Tutorial

Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at mr-mathematics.com.

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods