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Students learn how to recognise and prove various circle theorems including: angle at the centre is double the angle at the circumference, angles in the same segment are equal, opposite angles in cyclic quadrilaterals add to 180°, a tangent runs perpendicular to the radius and opposite angles in alternate segments are equal. This unit takes place in Term 6 of Year 10 and follows on from Angle Geometry.

**Prerequisite Knowledge**

- Understand and use alternate and corresponding angles on parallel lines;
- Derive and use the sum of angles in a triangle (e.g. to deduce use the angle sum in any polygon, and to derive properties of regular polygons)
- Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

**Success Criteria**

- Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
- Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

**Key Concepts**

- Students need a solid understanding of the properties for angles in parallel lines, vertically opposite, angles in a polygon and on a straight line.
- Understanding the various parts of a circle is critical to fully defining the various circle theorems.
- Students need to spend time breaking down the problem by considering the various angle properties that may be relevant.
- Taking time to prove the various theorems illustrates how interconnected all the properties are.
- Encourage students to annotate and draw on the diagrams.

**Common Misconceptions**

- Students often struggle with precisely defining the various angle the appropriate angle properties.
- Incomplete angle properties are a common source for losing marks in examinations.
- Angle and line notation often confuses students to an extent they may calculate an angle that was not asked for.
- Students need to relate their written work with the relevant angle rather than writing detached paragraphs.

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 […]