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GCSE / Maths

Geometry and Measures

Revise GCSE Maths Geometry and Measures, including constructions, angle rules, polygons, congruence, similarity, transformations, circle theorems, coordinate geometry, 2D and 3D shapes, area, volume, bearings, Pythagoras, trigonometry and vectors.

Geometry and measures in GCSE Maths covers geometric terminology, constructions, angles, polygons, transformations, circle geometry, coordinate geometry, 2D and 3D shapes, mensuration, trigonometry and vectors.
Geometry terminology includes points, lines, vertices, edges, faces, parallel lines, perpendicular lines, right angles and standard mathematical symbols used to describe geometric shapes and polygons.
Mathematical constructions in geometry use a ruler and compass to construct perpendicular bisectors, angle bisectors, perpendicular lines, 60° angles, loci and shortest-distance problems.
Angles and their properties include angles at a point, angles on a straight line, vertically opposite angles, alternate and corresponding angles, and angle sums in triangles and polygons.
Triangles and geometry include properties of isosceles, equilateral, scalene and right-angled triangles, while congruence uses SSS, SAS, ASA and RHS criteria and similarity compares shapes with matching angles and proportional sides.
Mathematical transformations include rotation, reflection, translation and enlargement, with fractional and negative scale factors, and combined transformations can be described by their overall effect.
Circle geometry and properties include centre, radius, diameter, circumference, chord, tangent, arc, sector and segment, while circle theorems connect angles, chords, tangents and cyclic quadrilaterals.
Coordinate geometry problems use coordinates in all four quadrants to solve geometric problems, while plans and elevations represent 3D shapes using accurate 2D views.
Standard measurement and unit conversion in geometry includes length, area, volume, capacity, mass and bearings, and three-figure bearings are measured clockwise from north.
For 2D and 3D geometric shapes calculations, use perimeter and area formulae for triangles, rectangles, circles and composite shapes, and volume formulae for cuboids, prisms, cylinders, pyramids, cones and spheres.
Circle and area calculations use circumference C=2πrC=2\pi r, area A=πr2A=\pi r^2, arc length θ360×2πr\frac{\theta}{360}\times2\pi r and sector area θ360×πr2\frac{\theta}{360}\times\pi r^2.
Similarity links corresponding lengths by a scale factor kk, corresponding areas by k2k^2 and corresponding volumes by k3k^3, which is essential in scale and scale conversion problems.
Pythagoras and triangle theorems use a2+b2=c2a^2+b^2=c^2 in right-angled triangles, while trigonometry concepts and formulas use sin⁡θ=oppositehypotenuse\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}, cos⁡θ=adjacenthypotenuse\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} and tan⁡θ=oppositeadjacent\tan\theta=\frac{\text{opposite}}{\text{adjacent}}.
For non-right-angled triangle geometry and calculations, use the sine rule asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}, the cosine rule a2=b2+c2−2bccos⁡Aa^2=b^2+c^2-2bc\cos A, and area A=12absin⁡CA=\frac{1}{2}ab\sin C.
Vector notation and math symbols describe translations and directed movement, and GCSE vector problems use addition, subtraction, scalar multiplication and vector geometry to construct arguments and proofs.
GCSE Geometry and Measures Revision | Think Study Learn