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4. Geometry

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  1. E4.1 Geometrical terms

    1. E4.1.1Geometrical terms

      • Use and interpret geometrical terms including point, vertex, line, plane, parallel, perpendicular, perpendicular bisector, bearing, angle types, similarity, congruence and scale factor.

    2. E4.1.2Shapes, polygons, nets and solids

      • Use and interpret the vocabulary of triangles, special quadrilaterals, regular and irregular polygons, nets and common solids including prisms, pyramids, cones, spheres, hemispheres and frustums.

    3. E4.1.3Circle vocabulary

      • Use and interpret circle vocabulary including centre, radius, diameter, circumference, semicircle, chord, tangent, major and minor arcs, sector and segment.

  2. E4.2 Geometrical constructions

    1. E4.2.1Measure and draw lines and angles.

      • Measure and draw lines and angles.

    2. E4.2.2Construct a triangle, given the lengths of all sides, using a ruler and

      • Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only.

    3. E4.2.3Draw, use and interpret nets

      • Draw, use and interpret nets. A ruler should be used for all straight edges. Constructions of perpendicular bisectors and angle bisectors are not required. e.g. construct a rhombus by drawing two triangles. Construction arcs must be shown. Examples include: • draw nets of cubes, cuboids, prisms and pyramids • use measurements from nets to calculate volumes and surface areas.

  3. E4.3 Scale drawings

    1. E4.3.1Draw and interpret scale drawings.

      • Draw and interpret scale drawings.

    2. E4.3.2Use and interpret three-figure bearings

      • Use and interpret three-figure bearings. A ruler must be used for all straight edges. Bearings are measured clockwise from north (000° to 360°). e.g. find the bearing of A from B if the bearing of B from A is 025°. Includes an understanding of the terms north, east, south and west. e.g. point D is due east of point C.

  4. E4.4 Similarity

    1. E4.4.1Calculate lengths of similar shapes.

      • Calculate lengths of similar shapes.

    2. E4.4.2Use the relationships between lengths and areas of similar shapes and

      • Use the relationships between lengths and areas of similar shapes and lengths, surface areas and volumes of similar solids.

    3. E4.4.3Solve problems and give simple explanations involving similarity

      • Solve problems and give simple explanations involving similarity. Includes use of scale factor, e.g. B A B A Volume of Volume of Lengtho f Lengtho f = ` `j j. Includes showing that two triangles are similar using geometric reasons.

  5. E4.5 Symmetry

    1. E4.5.1Line and rotational symmetry

      • Recognise line symmetry and order of rotational symmetry in two dimensions, including related properties of triangles, quadrilaterals and polygons.

    2. E4.5.2Symmetry of solids

      • Recognise planes and axes of symmetry of prisms, cylinders, pyramids and cones.

  6. E4.6 Angles

    1. E4.6.1Calculate unknown angles and give simple explanations using the

      • Calculate unknown angles and give simple explanations using the following geometrical properties: • sum of angles at a point = 360° • sum of angles at a point on a straight line = 180° • vertically opposite angles are equal • angle sum of a triangle = 180° and angle sum of a quadrilateral = 360°.

    2. E4.6.2Calculate unknown angles and give geometric explanations for angles

      • Calculate unknown angles and give geometric explanations for angles formed within parallel lines: • corresponding angles are equal • alternate angles are equal • co-interior angles sum to 180° (supplementary).

    3. E4.6.3Know and use angle properties of regular and irregular polygons

      • Know and use angle properties of regular and irregular polygons. Knowledge of 3-letter notation for angles is required, e.g. angle ABC. Candidates are expected to use the correct geometrical terminology when giving reasons for answers. Includes exterior and interior angles, and angle sum.

  7. E4.7 Circle theorems I

    1. E4.7.1

      • Calculate unknown angles and give explanations using the following geometrical properties of circles: • angle in a semicircle = 90° • angle between tangent and radius = 90° • angle at the centre is twice the angle at the circumference • angles in the same segment are equal • opposite angles of a cyclic quadrilateral sum to 180° (supplementary) • alternate segment theorem. Candidates are expected to use the geometrical properties listed in the syllabus when giving reasons for answers.

  8. E4.8 Circle theorems II

    1. E4.8.1

      • Use the following symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the centre • tangents from an external point are equal in length. Candidates are expected to use the geometrical properties listed in the syllabus when giving reasons for answers.