YEAR 8 MATHS FOCUS

For some students, formal setting out of proofs of congruent triangles could be introduced.

The meaning of the term ‘included angle’ should be taught explicitly. Similarly, the use of the adjective ‘matching’ when referring to the sides and angles of congruent shapes should be made explicit.

The term ‘corresponding’ is often used in relation to congruent and similar figures to refer to angles or sides in the same position, but it also has a specific meaning when used to describe a pair of angles in relation to lines cut by a transversal. This syllabus has used ‘matching’ to describe angles and sides in the same position; however, the use of the word ‘corresponding’ is not incorrect.

The term ‘superimpose’ is used to describe the placement of one figure upon another in such a way that the parts of one coincide with the parts of the other.

identify congruent figures by superimposing them through a combination of rotations, reflections and translations

• recognise congruent figures in tessellations, art and design work, eg mosaics (Reasoning)
• recognise that area, lengths of matching sides, and angle sizes are preserved in congruent figures (Reasoning)

investigate the minimum conditions needed, and establish the four tests, for two triangles to be congruent:

• • if the three sides of a triangle are respectively equal to the three sides of another triangle, then the two triangles are congruent (SSS test)
  • if two sides and the included angle of a triangle are respectively equal to two sides and the included angle of another triangle, then the two triangles are congruent (SAS test)
  • if two angles and one side of a triangle are respectively equal to two angles and the matching side of another triangle, then the two triangles are congruent (AAS test)
  • if the hypotenuse and a second side of a right-angled triangle are respectively equal to the hypotenuse and a second side of another right-angled triangle, then the two triangles are congruent (RHS test)
• use dynamic geometry software and/or geometrical instruments to investigate what information is needed to show that two triangles are congruent (Problem Solving)Information and communication technology capability Critical and creative thinking
• explain why the angle in the SAS test must be the included angle (Communicating, Reasoning)Critical and creative thinking
• demonstrate that three pairs of equal matching angles is not a sufficient condition for triangles to be congruent (Communicating, Reasoning)