Circle Theorems

June 16, 2023

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

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 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.

Common Misconceptions

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.

Circle Theorems Resources

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