Transformations and Symmetry

Prerequisite Knowledge

• Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
• Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D.

Key Concepts

• A mirror line or tracing paper can be used to check if a shape has a line of reflective symmetry.    A mirror line is called a line of reflective symmetry.
• Students tend to find reflections in a diagonal line of symmetry more difficult than those in horizontal or vertical.
• A plane of symmetry bisects a shape into halves that are mirror images of each other.
• A 2D shape has rotational symmetry if it can be rotated so that it fits perfectly on itself in a new position.
• The order of rotational is the number of positions the shape looks the same when it is rotated 360°.
• A translation vector is used to describe a translation.
• To rotate a shape a centre, direction and amount of turn is needed.  Students should use tracing paper when rotating shapes.
• A positive scale factor greater than 1 increases the size of a shape.  A postive scale factor less than one decreases the size.  More advanced students should enlarge a shape from a centre.
• Rotations, reflections and translations result in congruent shapes.  Enlargements result in similar shapes.

Working mathematically

Develop fluency

• Use language and properties precisely to analyse 2-D and 3-D shapes.

Reason mathematically

• Make and test conjectures about patterns and relationships; look for proofs or counter-examples
  Begin to reason deductively in geometry including using geometrical constructions

Solve problems

• Begin to model situations mathematically and express the results using a range of formal mathematical representations
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Geometry and measures

• 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
• Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
• Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
• Interpret mathematical relationships both algebraically and geometrically.