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# Category: Geometry Key stage 4

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Abbreviation: MG KS4

## Description

In addition to consolidating subject content from key stage 3, pupils should be taught to:

• interpret and use fractional {and negative} scale factors for enlargements
• {describe the changes and invariance achieved by combinations of rotations, reflections and translations}
• 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}
• construct and interpret plans and elevations of 3D shapes
• interpret and use bearings
• calculate arc lengths, angles and areas of sectors of circles
• calculate surface areas and volumes of spheres, pyramids, cones and composite solids
• apply the concepts of congruence and similarity, including the relationships between lengths, {areas and volumes} in similar figures
• apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures
• know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45°, 60°
• {know and apply the sine rule, = = , and cosine rule, a2 = b2 + c2 - 2bc cos A, to find unknown lengths and angles}
• {know and apply Area = ab sin C to calculate the area, sides or angles of any triangle}
• describe translations as 2D vectors
• apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}

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