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Geometry AQA GCSE (Mensuration and calculation (units of measure/concepts,…
Geometry
AQA GCSE
Properties and constructions
Constructions
Standard Constructions
perpendicular bisector
Concepts
know that the perpendicular distance from a point to a line is the shortest distance to the line
Solve
loci problems
construct given figures
Properties
terms and notations
#
#
draw diagrams from written description
conventions for labelling/refering to the sides and angles of triangles
polygons
polygons with reflection and/or rotation symmetries
regular
right angles
perpendicular lines
parallel lines
planes
edges
vertices
lines
points
Angles
#
Parallel Lines
Alternate
Corresponding
Opposite
Properties
angles at a point
angles at a point on a straight line
vertically opposite angles
sum of angles in a triangle
sum in any polygon
derive properties of regular polygons
Shapes
Quadrilaterals
Square
rectangle
parallelogram
trapezium
kite
rhombus
other plane figures
Triangles
names and properties
isosceles
#
equilateral
scalene
right-angled
acute-angled
obtuse-angled
congruence
#
SSS, SAS, ASA, RHS
polygons
hexagon
octagon
pentagon
decagon
proofs
pythagoras theorem
#
#
Circle theorems
#
angle subtended by an arc at the centre is equal to twice the angle subtended at any point on the circumference
angles in the same segment are equal
angle subtended at the circumference by a semicircle is 90°
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
describe/construct
congruent shapes
#
on coordinate axes
similar shapes
on coordinate axes
concepts
#
reflection
rotation
translation
vectors
describe translations as 2D vectors
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
enlargement
scale factors
fractional
negative
combinations
describe the changes and invariance
Solve
eometrical problems on coordinate axes
Circles
definitions/properties
radius
chord
diameter
circumference
tangent,
arc
sector
centre
segment
3d shapes
identify properties
#
surfaces
edges
vertices
faces
types
#
cubes
cuboids
prisms
cylinders
pyramids,
cones
spheres
Elevations
construct and interpret
Mensuration and calculation
units of measure/concepts
length
area
#
volume/capacity
mass
money
time
measuring
line segments
angles
scale drawings
bearings
three-figure bearings
eight compass point bearings
calculation
formulae
area
#
parallelograms
trapezia
volume of cuboids
#
other right prisms (including cylinders)
area of triangles
surface area and volume
#
spheres
pyramids
cones
composite solids
Circles
circumference
area
perimeter
area of sectors
arc lengths
angles
pythagoras
trigonometric ratios
sin tan cos = 0°, 30°, 45° , 60° and 90°
sine rule
cosine rule