YEAR 8 MATHS FOCUS
MEASUREMENT AND GEOMETRY
PROPERTIES OF GEOMETRIC FIGURES (PT 2)
- classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles
For some students, formal setting out of proofs of congruent triangles could be introduced.
|Dynamic geometry software and prepared applets are useful tools for investigating properties of congruent figures through transformations.|
|Congruent figures are embedded in a variety of designs, eg tapa cloth, Aboriginal designs, Indonesian ikat designs, Islamic designs, designs used in ancient Egypt and Persia, window lattice, woven mats and baskets.|
|Computer drawing programs enable students to prepare tessellation designs and to compare these with other designs, such as those of the Dutch artist M C Escher (1898–1972).|
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.
EXPECTATIONS OF ATTAINMENT
|Define congruence of plane shapes using transformations (ACMMG200)|
identify congruent figures by superimposing them through a combination of rotations, reflections and translations
|match sides and angles of two congruent polygons|
|name vertices in matching order when using the symbol|
≡ in statements regarding congruence
|determine the condition for two circles to be congruent (equal radii)|
Develop the conditions for congruence of triangles (ACMMG201)
investigate the minimum conditions needed, and establish the four tests, for two triangles to be congruent:
|use the congruency tests to identify a pair of congruent triangles from a selection of three or more triangles or from triangles embedded in a diagram|
Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (ACMMG202)
|apply the properties of congruent triangles to find an unknown side and/or angle in a diagram, giving a reason|
|use transformations of congruent triangles to verify some of the properties of special quadrilaterals, including properties of the diagonals, eg the diagonals of a parallelogram bisect each other|