**4.1 Angles, lines and triangles**

**A **distinguish between acute, obtuse, reflex and right angles

**B **use angle properties of intersecting lines, parallel lines and angles on a straight line

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

**D **understand the terms 'isosceles', 'equilateral' and 'right-angled triangles' and the angle properties of these triangles

**4.2 Polygons**

**A **recognise and give the names of polygons

**B **understand and use the term 'quadrilateral' and the angle sum property of quadrilaterals

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

**D **understand the term 'regular polygon' and calculate interior and exterior angles of regular polygons

**E **understand and use the angle sum of polygons

**F **understand congruence as meaning the same shape and size

**G **understand that two or more polygons with the same shape and size are said to be congruent to each other

**4.3 Symmetry**

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

**4.4 Measures**

**A **interpret scales on a range of measuring instruments

**B **calculate time intervals in terms of the 24-hour and the 12-hour clock

**C **make sensible estimates of a range of measures

**D **understand angle measure including three-figure bearings

**E **measure an angle to the nearest degree

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

**G **use compound measure such as speed, density and pressure

**4.5 Construction**

**A **measure and draw lines to the nearest millimetre

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

**C **solve problems using scale drawings

**D **use straight edge and compasses to:

(i) construct the perpendicular bisector of a line segment

(ii) construct the bisector of an angle

*E **understand and use the internal and external intersecting chord properties*

*F **recognise the term 'cyclic quadrilateral’*

*G **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*

**4.6 Circle properties**

**A **recognise the terms 'centre', 'radius', 'chord', 'diameter', 'circumference', 'tangent', 'arc', 'sector' and 'segment' of a circle

**B **understand chord and tangent properties of circles

**4.7 Geometrical reasoning**

**A **give informal reasons, where required, when arriving at numerical solutions to geometrical problems

*B **provide reasons, using standard geometrical statements, to support numerical values for angles obtained in any geometrical context involving lines, polygons and circles*

**4.8 Trigonometry and Pythagoras’ theorem**

**A **know, understand and use Pythagoras' theorem in two dimensions

**B **know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle

**C **apply trigonometrical methods to solve problems in two dimensions

*D **understand and use sine, cosine and tangent of obtuse angles*

*E **understand and use angles of elevation and depression*

*F **understand and use the sine and cosine rules for any triangle*

*G **use Pythagoras' theorem in three dimensions*

*H **understand and use the formula 1 ab sin C for the area of a triangle*

*I **apply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a plane*

**4.9 Mensuration of 2D shapes**

**A **convert measurements within the metric system to include linear and area units

**B **find the perimeter of shapes made from triangles and rectangles

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

**D **find the area of parallelograms and trapezia

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

*F **find perimeters and areas of sectors of circles*

**4.10 3D shapes and volume**

**A **recognise and give the names of solids

**B **understand the terms 'face', 'edge' and 'vertex' in the context of 3D solids

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

**D **find the surface area of a cylinder

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

**F **convert between units of volume within the metric system

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

**4.11 Similarity**

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

**B **use and interpret maps and scale drawings

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

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

*E **use areas and volumes of similar figures in solving pro*blems