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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.

- 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 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.

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

June 5, 2019

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values. Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]