Chapter 8.1
Angle properties (consolidation)
Review angles on lines, at a point, verticals, and angles in triangles.
Chapters14
Angles, circles, proofs, constructions, loci, and 3D geometry.
Time invested14 hrs
Approximate guided learning.
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Chapter 8.2
Angles in polygons (advanced)
Interior and exterior angles of regular and irregular polygons.
Chapter 8.3
Circle theorems (angles in same segment)
Angles subtended by the same arc are equal; angles and arc relationships.
Chapter 8.4
Circle theorems (angle at centre/circumference)
Angle at centre is twice the angle at circumference for same arc.
Chapter 8.5
Circle theorems (cyclic quadrilaterals)
Opposite angles in cyclic quadrilaterals sum to 180 degrees.
Chapter 8.6
Circle theorems (tangents)
Tangent properties: perpendicularity to radius and equal tangent lengths.
Chapter 8.7
Circle theorems (alternate segment)
Angle between tangent and chord equals inscribed angle in alternate segment.
Chapter 8.8
Circle theorem proofs
Develop formal proofs of key circle theorem results.
Chapter 8.9
Geometric proof with algebra
Combine algebraic expressions with geometry to prove general results.
Chapter 8.10
Bearings and scale drawings
Navigate using bearings; create and interpret scale drawings.
Chapter 8.11
Constructions (perpendiculars and bisectors)
Construct perpendiculars, angle bisectors, and perpendicular bisectors with ruler and compass.
Chapter 8.12
Loci (single conditions)
Find regions satisfying one distance or angle condition.
Chapter 8.13
Loci (multiple conditions)
Combine multiple conditions to find intersection regions in problem-solving.
Chapter 8.14
Plans and elevations
Visualise and draw 2D representations of 3D shapes.
Next steps
Master geometry reasoning? Move to Section 9 for trigonometric applications, or revisit Section 7 for coordinate geometry.