#G1
use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries
use the standard conventions for labelling and referring to the sides and angles of triangles
draw diagrams from written description
#G2
use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle)
use these to construct given figures and solve loci problems
know that the perpendicular distance from a point to a line is the shortest distance to the line
Notes: including constructing an angle of 60°.
#G3
apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
understand and use alternate and corresponding angles on parallel lines
derive and use the sum of angles in a triangle (eg to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)
Notes: colloquial terms such as Z angles are not acceptable and should not be used.
#G4
derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus
and triangles and other plane figures using appropriate language
Notes: including knowing names and properties of isosceles, equilateral, scalene, right-angled, acute-angled, obtuse-angled triangles.
Including knowing names and using the polygons: pentagon, hexagon, octagon and decagon.
#G5
use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
#G6
apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs
#G7
identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement
including fractional scale factors
including negative scale factors
#G8
describe the changes and invariance achieved by combinations of rotations, reflections and translations
Notes: including using column vector notation for translations. See also G24
#G9
identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference
including: tangent, arc, sector and segment
#G10
apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results
Notes: including angle subtended by an arc at the centre is equal to twice the angle subtended at any point on the circumference,
angle subtended at the circumference by a semicircle is 90°,
angles in the same segment are equal,
opposite angles in a cyclic quadrilateral sum to 180°,
tangent at any point on a circle is perpendicular to the radius at that point,
tangents from an external point are equal in length,
the perpendicular from the centre to a chord bisects the chord,
alternate segment theorem.
#G11
solve geometrical problems on coordinate axes
#G12
identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
#G13
interpret plans and elevations of 3D shapes
construct and interpret plans and elevations of 3D shapes
#G14
use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money etc.)
#G15
measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings
Notes: including the eight compass point bearings and three-figure bearings.
#G16
know and apply formulae to calculate: area of triangles, parallelograms, trapezia;
volume of cuboids and other right prisms (including cylinders)
#G17
know the formulae: circumference of a circle \(=2\pi r = \pi d\)
area of a circle \(= \pi r^2\)
calculate perimeters of 2D shapes, including circles
areas of circles and composite shapes
surface area and volume of spheres, pyramids, cones and composite solids
Notes: including frustums.
Solutions in terms of \(\pi\) may be asked for. See also N8, G18
#G18
calculate arc lengths, angles and areas of sectors of circles
Notes: see also N8, G17
#G19
apply the concepts of congruence and similarity, including the relationships between lengths in similar figures
including the relationships between lengths, areas and volumes in similar figures
Notes: see also R12
#G20
know the formulae for: Pythagoras’ theorem, \(a^2+b^2=c^2\)
and the trigonometric ratios,
\(\sin{\theta}=\dfrac{opposite}{hypotenuse}\),
\(\cos{\theta}=\dfrac{adjacent}{hypotenuse}\) and
\(\tan{\theta}=\dfrac{opposite}{adjacent}\)
apply them to find angles and lengths in right-angled triangles in two dimensional figures
apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures
Notes: see also R12
#G21
know the exact values of \(\sin{\theta}\) and \(\cos{\theta}\) for \(\theta = 0°, 30°, 45° , 60°, 90° \)
know the exact value of \(\tan{\theta}\) for \(\theta = 0°, 30°, 45°, 60° \)
Notes: see also A12
#G22
know and apply the sine rule,
\(\dfrac{a}{\sin{A}} = \dfrac{b}{\sin{B}} = \dfrac{c}{\sin{C}} \)
and cosine rule,
\(a^2 = b^2 + c^2 - 2bc\cos{A} \)
to find unknown lengths and angles
#G23
know and apply
\(\text{Area} = \dfrac{1}{2}ab\sin{C} \)
to calculate the area, sides or angles of any triangle
#G24
describe translations as 2D vectors
Notes: see also G8
#G25
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