4 Geometry and trigonometry
Start with Concept to understand a topic, then use Question Bank to check what you know.
Your progress
Sign in to see your mastery and mistakes.
4.1 Angles, lines and triangles
4.1.ADistinguish between acute, obtuse, reflex and right
distinguish between acute, obtuse, reflex and right angles
4.1.BAngle properties of intersecting lines, parallel lines
use angle properties of intersecting lines, parallel lines and angles on a straight line Angles at a point, vertically opposite angles, alternate angles, corresponding angles, allied angles
4.1.CThe exterior angle of a triangle property and the angle
understand the exterior angle of a triangle property and the angle sum of a triangle property
4.1.DThe terms ‘isosceles’, ‘equilateral’ and ‘right-angled
understand the terms ‘isosceles’, ‘equilateral’ and ‘right-angled triangles’ and the angle properties of these triangles
4.2 Polygons
4.2.ANames of polygons
Recognise and name parallelograms, rectangles, squares, rhombuses, trapeziums, kites, pentagons, hexagons and octagons.
4.2.BQuadrilaterals and their angle sum
understand and use the term ‘quadrilateral’ and the angle sum property of quadrilaterals The four angles of a quadrilateral are 90°, (x + 15)°, (x +25)° and (x + 35)° Find the value of x
4.2.CProperties of quadrilaterals
understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite
4.2.DRegular polygons and their angles
understand the term ‘regular polygon’ and calculate interior and exterior angles of regular polygons
4.2.EAngle sum of polygons
understand and use the angle sum of polygons For a polygon with n sides, the sum of the interior angles is (2n – 4) right angles
4.2.FCongruence as meaning the same shape and size
understand congruence as meaning the same shape and size
4.2.GCongruent polygons
Understand that polygons with the same shape and size are congruent.
4.3 Symmetry
4.3.A
identify lines of symmetry and the order of rotational symmetry of a given two-dimensional figure
4.4 Measures
4.4.AScales on a range of measuring instruments
interpret scales on a range of measuring instruments
4.4.BTime intervals in terms of the 24-hour and the 12-hour
calculate time intervals in terms of the 24-hour and the 12-hour clock Use am and pm
4.4.CMake sensible estimates of a range of measures
make sensible estimates of a range of measures
4.4.DAngle measure
understand angle measure including three-figure bearings
4.4.EMeasure an angle to the nearest degree
measure an angle to the nearest degree
4.4.FAverage speed, distance and time
understand and use the relationship between average speed, distance and time
4.4.GCompound measure such as speed, density and pressure
use compound measure such as speed, density and pressure Formula for pressure will be given
4.5 Construction
4.5.AMeasure and draw lines to the nearest millimetre
measure and draw lines to the nearest millimetre
4.5.BConstructing two-dimensional shapes
construct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses
4.5.CProblems using scale drawings
solve problems using scale drawings
4.5.DPerpendicular and angle bisectors
use straight edge and compasses to: (i) construct the perpendicular bisector of a line segment (ii) construct the bisector of an angle
4.6 Circle properties
4.6.ACircle terminology
Recognise the centre, radius, chord, diameter, circumference, tangent, arc, sector and segment of a circle.
4.6.BChord and tangent properties of circles Two tangents
understand chord and tangent properties of circles Two tangents from a point to a circle are equal in length Tangents are perpendicular to the radius at the point of contact The line from the centre of a circle which is perpendicular to a chord bisects the chord (and the converse)
4.6.HAIntersecting chord properties
understand and use the internal and external intersecting chord properties
4.6.HBThe term ‘cyclic quadrilateral’
recognise the term ‘cyclic quadrilateral’
4.6.HCCircle angle properties
understand and use angle properties of the circle including: (i) angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the remaining part of the circumference (ii) angle subtended at the circumference by a diameter is a right angle (iii) angles in the same segment are equal (iv) the sum of the opposite angles of a cyclic quadrilateral is 180° (v) the alternate segment theorem Formal proof of these theorems is not required
4.7 Geometrical reasoning
4.7.AGive informal reasons, where required, when arriving at
give informal reasons, where required, when arriving at numerical solutions to geometrical problems Reasons will only be required for geometrical calculations based on lines (including chords and tangents), triangles or polygons
4.7.HAGeometrical reasoning for angles
Use standard geometrical statements to justify angle values in contexts involving lines, polygons and circles.
4.8 Trigonometry and Pythagoras’ theorem
4.8.APythagoras' theorem in two dimensions
know, understand and use Pythagoras’ theorem in two dimensions
4.8.BTrigonometry in right-angled triangles
know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle
4.8.CTwo-dimensional trigonometry and bearings
Apply trigonometric methods to solve two-dimensional problems, including bearings.
4.8.HATrigonometric ratios of obtuse angles
understand and use sine, cosine and tangent of obtuse angles
4.8.HBAngles of elevation and depression
understand and use angles of elevation and depression
4.8.HCSine and cosine rules
understand and use the sine and cosine rules for any triangle
4.8.HDPythagoras’ theorem in three dimensions
use Pythagoras’ theorem in three dimensions
4.8.HEArea of a triangle using 1/2 ab sin C
understand and use the formula ½ab sin C for the area of a triangle
4.8.HFTrigonometrical methods to solve problems in three
apply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a plane The angle between two planes will not be required
4.9 Mensuration of 2D shapes
4.9.AMeasurements within the metric system
convert metric measurements, including linear and area units such as cm² and m²
4.9.BPerimeters of triangles and rectangles
find the perimeter of shapes made from triangles and rectangles
4.9.CAreas of triangles and rectangles
find the area of simple shapes using the formulae for the areas of triangles and rectangles
4.9.DThe area of parallelograms and trapezia
find the area of parallelograms and trapezia
4.9.ECircumferences and areas of circles using relevant
find circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles
4.9.HAPerimeters and areas of sectors of circles Radian
find perimeters and areas of sectors of circles Radian measure is excluded
4.10 3D shapes and volume
4.10.ANames of solids
Recognise and name cubes, cuboids, prisms, pyramids, cylinders, spheres and cones.
4.10.BFaces, edges and vertices
understand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids
4.10.CThe surface area of simple shapes using the area
find the surface area of simple shapes using the area formulae for triangles and rectangles
4.10.DThe surface area of a cylinder
find the surface area of a cylinder
4.10.EThe volume of prisms
find the volume of prisms, including cuboids and cylinders, using an appropriate formula
4.10.FBetween units of volume within the metric system
convert between metric units of volume, including cm³ and m³, and use 1 litre = 1000 cm³
4.10.HAThe surface area and volume of a sphere and a right
find the surface area and volume of a sphere and a right circular cone using relevant formulae
4.11 Similarity
4.11.AGeometrical properties of similar figures
understand and use the geometrical properties that similar figures have corresponding lengths in the same ratio but corresponding angles remain unchanged
4.11.BMaps and scale drawings
Use and interpret maps and scale drawings.
4.11.HAArea scale factors
understand that areas of similar figures are in the ratio of the square of corresponding sides
4.11.HBVolume scale factors
understand that volumes of similar figures are in the ratio of the cube of corresponding sides
4.11.HCAreas and volumes of similar figures
Use the areas and volumes of similar figures to solve problems.