Below there are 241 Geometry & Measures Topics
Geometry & Measures are probably the most incorrectly answered or missed out areas in GCSE Maths
These areas are very important for solving problems and getting the higher grades! It's common to see them mixed with Algebra.
Step 01
Geometry & Measures
Key Stage 2 - GCSE Basics
- Explain why some shapes tessellate and why other shapes do not
- Tessellate combinations of polygons
- Know the sum of angles on a straight line
- Find the perimeter of a square/rectangle by counting
- Know the terms face, edge and vertex
- Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone
- Identify complex arrangements of a net of an open cube
- Identify more complex arrangement of a net of a closed cube
- Work out time intervals
- Read and interpret scales on a range of measuring instruments
- Record readings from scales to a suitable degree of accuracy
- Suggest suitable units to estimate or measure length, mass and capacity
- Identify all the symmetries of 2-D shapes
- Recognise properties of rectangles
- Recognise properties of squares
- Draw sketches of shapes
- Scale a shape on a grid (without a centre specified)
- Understand and use the language associated with reflections
- Understand and use the language associated with translations
- Recognise where a shape will be after reflection
Step 02
Geometry & Measures
Key Stage 2 - GCSE Basics
- Use a protractor to measure acute angles to the nearest degree
- Measure lines to the nearest millimetre
- Know the sum of angles round a point
- Identify parallel lines
- Find the perimeter of a square/rectangle
- Construct diagrams of everyday 2-D situations involving rectangles, triangles, perpendicular and parallel lines
- Know and use geometric properties of cuboids
- Choose suitable metric units to estimate length and area.
- Understand that area is measured in square centimetres
- Draw parallel lines
- Mark parallel lines on a diagram
- Identify quadrilaterals from everyday usage
- Know the sum of angles in a triangle is 180°
- Use correct notation for labelling lines
- Recognise reflection symmetry
- Understand and use the language associated with rotations
- Recognise where a shape will be after translation
- Translate a shape on a square/coordinate grid
- Recognise and visualise the reflection in a mirror line of a 2-D shape
Step 03
Geometry & Measures
Key Stage 2 - GCSE Basics
- Use correct notation for labelling angles
- Distinguish between acute and obtuse angles
- Distinguish between acute, obtuse and reflex angles
- Identify perpendicular lines
- Use the formula for the area of a rectangle/square
- Calculate the surface area of cubes with a net
- Use nets to calculate the surface area of simple cuboids
- Calculate perimeter and area of compound shapes made from triangles, rectangles and other shapes
- Identify different nets of a cuboid
- Know and use geometric properties of shapes made from cuboids
- Record estimates to a suitable degree of accuracy
- Use units of measurement to estimate and solve problems in everyday contexts involving length, area, volume, mass, time and angle
- Know that measurements using real numbers depend upon the choice of unit
- Use correct notation for labelling triangles
- Mark perpendicular lines on a diagram
- Recognise and visualise the symmetry of a 2-D shape: line symmetry
- Calculate angles in a triangle
- Identify simple angle, side and symmetry properties of triangles
- Identify angle, side and symmetry properties of simple quadrilaterals
- Recognise and visualise – rotation about a given point (rotation point must be outside the shape)
- Begin to estimate the size of angles
- Use a protractor to measure obtuse angles to the nearest degree
- Use a protractor to draw acute angles to the nearest degree
- Use a protractor to measure reflex angles to the nearest degree
- Measure shapes to find (perimeters and) areas
Step 04
Geometry & Measures
Key Stage 3 - Pre GCSE
- Identify interior and exterior angles in a shape
- Know the definition of a set of lines which are perpendicular to each other
- Calculate angles around a point
- Recognise and use vertically opposite angles
- Use sum of angles in a triangle to find missing angle values
- Derive and use the sum of angles in a triangle and a quadrilateral
- Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles
- Use the sum of the interior angle and the exterior angle is 180°
- Calculate the area of simple shapes made from rectangles
- Calculate the area of more complex shapes made from rectangles
- Calculate the surface area of cubes, without a net
- Calculate the perimeter and area of shapes made from rectangles
- Calculate the surface area of simple cuboids (without use of nets)
- Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
- Use ruler and protractor to construct simple nets of 3D shapes, using squares, rectangles and triangles, e.g. regular tetrahedron, square-based pyramid, triangular prism
- Begin to use plans and elevations
- Solve simple problems involving units of measurement in the context of length and area
- Use geometric language appropriately
- Identify regular and irregular polygons
- Draw or complete diagrams with a given number of lines of symmetry
- Draw or complete diagrams with a given order of rotational symmetry
- Recognise and visualise the rotational symmetry of a 2-D shape
- Identify and plot points determined by geometric information
- Find co-ordinates of points determined by geometric information
- Solve geometric problems using side and angle properties of equilateral and isosceles triangles
- List the properties of each, or identify (name) a given shape
- Name all quadrilaterals that have a specific property
- Solve simple geometrical problems using properties of triangles
- Solve simple geometrical problems using properties of quadrilaterals
- Identify and begin to use angle, side and symmetry properties of quadrilaterals
- Use a protractor to draw obtuse angles to the nearest degree
- Use a protractor to draw reflex angles to the nearest degree
- Understand and use the language associated with bearings
- Use bearing to specify direction
- Give a bearing between the points on a map or scaled plan
Step 05
Geometry & Measures
Key Stage 3 - Pre GCSE
- Solve harder problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons - by looking at several shapes together
- Identify alternate and corresponding angles on parallel lines and their values.
- Find the area of triangles by counting i.e. adding full and partial squares
- Know the formulae for the volume of cube and a cuboid
- Use a formula to calculate the area of parallelograms
- Use a formula to calculate the area of triangles
- Deduce and use formulae for the area of a triangle
- Calculate areas of compound shapes made from rectangles and triangles
- Know and understand the term 'congruent'
- Know that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not.
- Know that translations, rotations and reflections map objects on to congruent images
- Identify simple nets of 3D shapes – regular polyhedra
- Use straight edge and compasses to construct the mid point and perpendicular bisector of a line segment
- Draw a circle given the radius or diameter
- Know that translations, rotations and reflections preserve length and angle
- Recognise that enlargements preserve angle but not length
Step 06
Geometry & Measures
Key Stage 3 - Pre GCSE
- Given the bearing of point A from point B, work out the bearing of B from A
- Identify co-interior angles and their values.
- Use the sum of the exterior angles of any polygon is 360°
- Calculate the interior angles of regular polygons
- Use the sum of angles in a triangle to deduce and use the angle sum in any polygon
- Deduce and use the formula for the area of a parallelogram
- Use a formula to calculate the area of trapezia
- Deduce and use formula for the area of a trapezium
- Calculate surface areas of shapes made from cuboids, for lengths given as whole numbers
- Know the formulae for the circumference and area of a circle
- Use the formula for the circumference of a circle
- Use the formulae for area of a circle, given the radius or diameter
- Identify congruent shapes
- Identify 2-D shapes that are congruent or similar by reference to sides and angles
- Identify shapes which are similar, including all regular polygons with equal number of sides
- Recognise that all corresponding angles in similar shapes are equal in size when the corresponding lengths of sides are not equal in size
- Identify more complex nets of 3D shapes including irregular polyhedra.
- Deduce properties of simple 3D shapes from their 2D representations
- Analyse 3-D shapes through 2-D representations.
- Analyse 3-D shapes through cross-sections, plans and elevations
- Draw plans and elevations of 3-D shapes
- Use straight edge and compasses to construct the bisector of an angle
- Use straight edge and compasses to construct a triangle given three sides (SSS)
- Construct an equilateral triangle
- Construct a regular hexagon inside a circle
- Begin to use the trigonometric ratios to find the size of an angle in a right-angled triangle
- Draw and label diagrams from given instructions
- Solve geometric problems using side and angle properties of equilateral, isosceles and right-angled triangles
- Know the names of parts of a circle
- Know the definition of a circle
- Draw circles and arcs to a given radius
- Enlarge 2-D shapes, given a centre of enlargement and a positive whole number scale factor
- Explore enlargement using ICT
- Enlarge a given shape using (0, 0) as the centre of enlargement
- Enlarge shapes with a centre other than (0, 0)
- Find the centre of enlargement
Step 07
Geometry & Measures
KS4 - Foundation GCSE
- Mark on a diagram the position of point B given its bearing from the point A
- Use accurate drawing to solve bearings problems
- Use the sum of the interior angles of an n-sided polygon
- Calculate the interior angles of polygons
- Find the size of each interior angle or the size of each exterior angle or the number of sides of a regular polygon
- Calculate volumes of shapes made from cuboids, for lengths given as whole numbers
- Calculate the volume of right prisms
- Calculate the surface area of right prisms
- Calculate the lengths and areas given the volumes in right prisms
- Calculate the lengths, areas and volumes in cylinders
- Use the formulae for the circumference and area of a circle, given the circumference or area, to calculate the radius or diameter
- Find the perimeters and areas of semicircles and quarter circles
- Begin to use congruency to solve simple problems in triangles and quadrilaterals
- Use the information given about the length of sides and sizes of angles to determine whether triangles are congruent, or similar
- Use straight edge and compass to construct the perpendicular from or to a point on a line segment
- Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS)
- Draw the locus equidistant between 2 points or from a point
- Produce shapes and paths by using descriptions of loci
- Use construction to find the locus of a point that moves according to a rule
- Understand loci about a point, line and corner.
- Construct angles of 60°, 90°, 30°, 45°
- Know the formula for Pythagoras' theorem and use to find the hypotenuse
- Know that the perpendicular distance from a point to a line is the shortest distance to the line
- Justify if a triangle is right-angled given its three lengths
- Use vector notation for translations
- Use 2D Vector notation for translation
- Understand and use the language and notation associated with enlargement
- Enlarge 2D shapes, given a fractional scale factor
- Find the centre of rotation
- Describe a transformation
- Describe reflections on a coordinate grid
- Colour in missing squares to complete a reflection
- Recognise whether a reflection is correct
- Express points as position vectors
- Understand and use vector notation
Step 08
Geometry & Measures
KS4 - Foundation GCSE
- Find the surface area of simple shapes (prisms) using the formulae for triangles and rectangles, and other shapes
- Find the surface area and volumes of compound solids constructed from cubes, cuboids, cones, pyramids, spheres, hemispheres, cylinders
- Recognise the formulae for length of arcs in a circle.
- Recognise the formulae for area of sectors in a circle.
- Solve problems involving angles, triangles and circles
- Use similarity to solve problems in 2D shapes
- Use simple examples of the relationship between enlargement and areas and volumes of simple shapes and solids
- Understand that a locus in 3D can be a plane or curved surface and extend understanding of loci to include 3D problems, e.g. know that all the points equidistant from a single point in space
form the surface of a sphere
- Understand how standard constructions using straight edge and compasses relate to the properties of two intersecting circles with equal radii
- Know the formula for Pythagoras' theorem and use to find a shorter side
- Use and apply Pythagoras' theorem to solve problems
- Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle, using straight-forward algebraic manipulation, e.g. calculate the adjacent (using cosine),
or the opposite (using sine or tangent ratios)
- Understand the language of planes, and recognise the diagonals of a cuboid
- Derive the fact that base angles of isosceles triangles are equal
- Transform 2-D shapes by simple combinations of rotations, reflections and translations, using ICT (e.g. repeated reflection, rotation or translation, reflections in the x and y axes, rotations
about (0, 0))
- Transform 2D shapes by a more complex combinations of rotations, reflections and translations, e.g. a reflection, followed by a rotation etc
- Add and Subtract vectors
Step 09
Geometry & Measures
KS4 - Foundation GCSE
- Prove and use the fact that the angle in a semicircle is a right angle ;
- Prove and use the fact that angles in the same segment are equal
- Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180°
- Prove and use facts about the angle subtended at the centre and at the circumference;
- Use the sine, cosine and tangent ratios to find the lengths of unknown sides in a right-angled triangle, using more complex algebraic manipulation, e.g. the hypotenuse (using cosine or sine),
or adjacent (using the tangent ratio)
- Use the appropriate ratio to find a length, or angle, and hence solve a two-dimensional problem
- Find angles of elevation and angles of depression
- Know that the tangent at any point on a circle is perpendicular to the radius at that point
- Know that the perpendicular from the centre to the chord bisects the chord
- Complete a formal geometric proof of similarity of two given triangles
Step 10
Geometry & Measures
Key Stage 4 - Higher GCSE
- Solve problems including examples of solids in everyday use
- Prove and use the alternate segment theorem
- Use congruence to show that translations, rotations and reflections preserve length and angle, so that any figure is congruent to its image under any of these transformations
- Understand, recall and use Pythagoras' theorem in 3-D problems
- Calculate the length of a diagonal of a cuboid
- Enlarge 2D shapes, given a negative, fractional scale factor
- Know and apply the sine rule a/sin A = b/sin B = c/sin C to find unknown lengths and angles
- Know and apply the cosine rule a² = b² + c² – 2bc cos A to find unknown lengths
- Calculate the area of a triangle given the length of two sides and the included angle
- Work out the magnitude of a vector
- Calculate, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector
- Calculate the resultant of two vectors
- Solve geometrical problems in 2-D using vector methods
Step 11
Geometry & Measures
Key Stage 4 - Higher GCSE
- Use the formulae for length of arcs and area of sectors of circles to solve problems
- Give reasons for angle sizes using mathematical language
- Give reasons for angle and length calculations involving the use of tangent theorems
- Understand and use the fact that tangents from an external point are equal in length
- Know and apply the cosine rule a² = b² + c² – 2bc cos A to find unknown angles
- Know and apply Area = 1/2 ab sin C to calculate the sides or angles of any triangle
- Prove lines are parallel/colinear
Step 12
Geometry & Measures
Key Stage 4 - Higher GCSE
- Solve problems involving more complex shapes and solids, including segments of circles and frustums of cones
- Find the area of a segment of a circle given the radius and length of the chord
- Solve problems for areas and volumes of similar shapes and solids
- Use the trigonometric ratios to solve 3-D problems
- Find the angle between a line and a plane (but not the angle between two planes or between two skew lines)
- 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° and 60°
- Use the sine and cosine rules to solve 2-D and 3-D problems
- Apply vector methods for simple geometrical proofs
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