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**Scheme of work: GCSE Higher: Year 10: Term 6: Circle Theorems**

- 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

- 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

- Students need a solid understanding of the properties of 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.

- Students often struggle with precisely defining the various angle 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.

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