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5.6 Symmetry in three-dimensional shapes

3 The diagram shows an L-shaped prism. 2 cm
a How many faces does it have? 2 cm
b Draw the object on isometric paper. 2 cm
c The prism has a plane of symmetry. 3 cm
Show it on your isometric drawing.
4 cm 2 cm

5 cm

4 a Draw a cube. Show a plane of symmetry that passes through four edges but no vertices.
b Draw the cube again. Show a plane of symmetry that passes through four vertices of the cube.

5 a Draw a cylinder.
b Draw a plane of symmetry that passes through the circular ends of the cylinder.
c Draw a plane of symmetry that does not pass through the circular ends of the cylinder.

Summary

You should now know that: You should be able to:
+ The angles of a regular polygon are all the same + Calculate the interior and exterior angle of any
size and the sides are all the same length. regular polygon.

+ The sum of the interior angles of a polygon with N + Prove the formula for the sum of the interior
sides is (N − 2) × 180°. angles of any polygon and that the sum of the
+ The sum of the exterior angles of a polygon exterior angles is 360°.
is 360°. + Solve problems by using properties of angles, of
+ The angle properties of parallel lines and polygons parallel and intersecting lines, and of triangles,
can be used to solve problems about angles and other polygons and circles, and explain reasoning.
explain reasoning. + Draw 3D shapes on isometric paper.
+ Three-dimensional shapes can be shown as + Analyse 3D shapes through plans and elevations.
diagrams on isometric paper or by drawing plans + Draw a plane of symmetry on a three-dimensional
and elevations. shape.
+ Three-dimensional shapes can have reflection + Recognise and use spatial relationships in two
symmetry. dimensions and three dimensions.
+ Draw accurate mathematical diagrams.
+ Present arguments to justify solutions or
generalisations, using symbols and diagrams or
graphs and related explanations.

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