Chapter 8.1
Angle properties (review and mastery)
Review all fundamental angle properties and apply to complex problems.
Chapters16
Angles, circle theorems, bearings, geometric proof.
Time invested12 hrs
Approximate guided learning.
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Chapter 8.2
Angles in parallel lines
Master alternate, corresponding, and co-interior angles.
Chapter 8.3
Angles in triangles and quadrilaterals
Calculate missing angles using angle sum properties.
Chapter 8.4
Angles in polygons (interior and exterior)
Apply polygon angle formulae to regular and irregular shapes.
Chapter 8.5
Bearings (all types)
Calculate three-figure bearings and solve navigation problems.
Chapter 8.6
Circle parts and definitions
Learn the vocabulary of circles: chord, tangent, sector, segment.
Chapter 8.7
Circle theorems - angles in same segment
Angles subtended by the same arc are equal.
Chapter 8.8
Circle theorems - angle at centre
The angle at the centre is twice the angle at the circumference.
Chapter 8.9
Circle theorems - angles in a semicircle
Any angle in a semicircle is a right angle.
Chapter 8.10
Circle theorems - cyclic quadrilaterals
Opposite angles in cyclic quadrilaterals sum to 180°.
Chapter 8.11
Circle theorems - tangents
A tangent meets a radius at 90°; two tangents from a point are equal.
Chapter 8.12
Circle theorems - alternate segment
The angle between tangent and chord equals angle in alternate segment.
Chapter 8.13
Circle theorem proofs
Construct formal proofs for circle theorems using logical reasoning.
Chapter 8.14
Plans and elevations
Draw and interpret plans and elevations of 3D shapes.
Chapter 8.15
Geometric proof
Write formal geometric proofs using deductive reasoning.
Chapter 8.16
Geometry problem-solving
Combine all geometry skills to tackle complex GCSE problems.
Next steps
Ready for Pythagoras and trigonometry? Continue to Section 9, or revisit Section 7 for graphs.