4.1 Properties and constructions
4.1.1 use conventional terms and notations; use the
standard conventions for labelling and referring to
the sides and angles of triangles; draw diagrams
from written description
4.1.2 use the standard ruler and
compass constructions ; use
these to construct given figures
and solve loci problems
4.1.3 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
4.1.4 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
4.1.5 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
4.1.6 use the basic
congruence
criteria for
triangles (SSS,
SAS, ASA, RHS)
4.1.7 identify, describe and construct congruent and similar
shapes, including on coordinate axes, by considering
rotation, reflection, translation and enlargement
(including fractional and negative scale factors)
4.1.8 identify and apply circle definitions and properties,
including: centre, radius, chord, diameter,
circumference, tangent, arc, sector and segment
4.1.9 describe the
changes and
invariance
achieved by
combinations of
rotations,
reflections and
translations
4.1.10 apply and prove the standard circle theorems concerning angles,
radii, tangents and chords, and use them to prove related results
4.1.11 identify properties of the faces,
surfaces, edges and vertices of:
cubes, cuboids, prisms, cylinders,
pyramids, cones and spheres
4.1.12 solve geometrical
problems on
coordinate axes
4.1.13 construct and interpret plans
and elevations of 3D shapes.
4.2 Mensuration and calculation
4.2.1 use standard units of measure
and related concepts (length,
area, volume/capacity, mass,
time, money, etc.)
4.2.2 measure line segments and angles in
geometric figures, including interpreting
maps and scale drawings and use of bearings
4.2.3 know and apply formulae to calculate:
area of triangles, parallelograms,
trapezia; volume of cuboids and other
right prisms (including cylinders)
4.2.4 know the formulae: circumference of a circle = 2πr = πd, area
of a circle = πr2; calculate: perimeters of 2D shapes, including
circles; areas of circles and composite shapes; surface area
and volume of spheres, pyramids, cones and composite solids
4.2.5 calculate arc lengths,
angles and areas of
sectors of circles
4.2.6 apply the concepts of congruence and
similarity, including the relationships
between lengths, areas and volumes in
similar figures
4.2.7 know the formulae for: Pythagoras’ theorem and
the trigonometric ratios, sinθ = opposite hypotenuse
, cosθ = adjacent hypotenuse and tanθ = opposite
adjacent ; apply them to find angles and lengths in
right-angled triangles and, where possible, general
triangles in two and three dimensional figures
4.2.8 know the exact
values of sinθ and
cosθ for given
values of θ (see
attached)
4.2.9 know and apply the sine rule
and cosine rule, to find
unknown lengths and angles
4.2.10 know and apply Area
= 1/2 ab SinC to
calculate the area,
sides or angles of any
triangle.