4 Geometry and trigonometry

distinguish between acute, obtuse, reflex and right angles

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

understand the exterior angle of a triangle property and the angle sum of a triangle property

understand the terms ‘isosceles’, ‘equilateral’ and ‘right-angled triangles’ and the angle properties of these triangles

Recognise and name parallelograms, rectangles, squares, rhombuses, trapeziums, kites, pentagons, hexagons and octagons.

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

understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite

understand the term ‘regular polygon’ and calculate interior and exterior angles of regular 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

understand congruence as meaning the same shape and size

Understand that polygons with the same shape and size are congruent.

identify lines of symmetry and the order of rotational symmetry of a given two-dimensional figure

interpret scales on a range of measuring instruments

calculate time intervals in terms of the 24-hour and the 12-hour clock Use am and pm

make sensible estimates of a range of measures

understand angle measure including three-figure bearings

measure an angle to the nearest degree

understand and use the relationship between average speed, distance and time

use compound measure such as speed, density and pressure Formula for pressure will be given

measure and draw lines to the nearest millimetre

construct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses

solve problems using scale drawings

use straight edge and compasses to: (i) construct the perpendicular bisector of a line segment (ii) construct the bisector of an angle

Recognise the centre, radius, chord, diameter, circumference, tangent, arc, sector and segment of a circle.

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)

understand and use the internal and external intersecting chord properties

recognise the term ‘cyclic quadrilateral’

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

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

Use standard geometrical statements to justify angle values in contexts involving lines, polygons and circles.

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

convert metric measurements, including linear and area units such as cm² and m²

find the perimeter of shapes made from triangles and rectangles

find the area of simple shapes using the formulae for the areas of triangles and rectangles

find the area of parallelograms and trapezia

find circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles

find perimeters and areas of sectors of circles Radian measure is excluded

Recognise and name cubes, cuboids, prisms, pyramids, cylinders, spheres and cones.

understand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids

find the surface area of simple shapes using the area formulae for triangles and rectangles

find the surface area of a cylinder

find the volume of prisms, including cuboids and cylinders, using an appropriate formula

convert between metric units of volume, including cm³ and m³, and use 1 litre = 1000 cm³

find the surface area and volume of a sphere and a right circular cone using relevant formulae

understand and use the geometrical properties that similar figures have corresponding lengths in the same ratio but corresponding angles remain unchanged

Use and interpret maps and scale drawings.

understand that areas of similar figures are in the ratio of the square of corresponding sides

understand that volumes of similar figures are in the ratio of the cube of corresponding sides

Use the areas and volumes of similar figures to solve problems.