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KS3 - Geometry and Measures

Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

<Area of a triangle>   <Finding the area of a composite shape>  <Area parallelogram>   

<Area of a kite>   <Area of a trapezium>   <Area of a circle>   <Volume of a cuboids>

Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

<Circumference of a circle>

Draw and measure line segments and angles in geometric figures, including interpreting scale drawings

<Draw angles>

Derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

Use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

<Classify quadrilaterals>

Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

<Translations>   <Rotations>   <Reflections>

Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

<Enlargements>

Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

<Angles on a straight line>   <Angles around a point>

Understand and use the relationship between parallel lines and alternate and corresponding angles

<Alternate angles>

Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

<Triangles>    <Polygons>   <Polygons>

Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs

Use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

Interpret mathematical relationships both algebraically and geometrically





The National Curriculum KS3 requirements are shown below in blue text. Underneath each of these requirements work helping to address ideas involved can be viewed by clicking on the bold underlined titles.