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NSW Syllabuses

Mathematics K–10 - Stage 5.1 - Measurement and Geometry Properties of Geometrical Figures

Outcomes

A student:

  • MA5.1-1WM

    uses appropriate terminology, diagrams and symbols in mathematical contexts

  • MA5.1-2WM

    selects and uses appropriate strategies to solve problems

  • MA5.1-3WM

    provides reasoning to support conclusions that are appropriate to the context

  • MA5.1-11MG

    describes and applies the properties of similar figures and scale drawings

Related Life Skills outcomes: MALS-32MG, MALS-33MG, MALS-34MG

 

Content

  • describe two figures as similar if an enlargement of one is congruent to the other L
  • recognise that if two figures are similar, they have the same shape but are not necessarily the same size (Reasoning)
  • find examples of similar figures embedded in designs from many cultures and historical periods (Reasoning) IU
  • explain why any two equilateral triangles, or any two squares, are similar, and explain when they are congruent (Communicating, Reasoning) CCT
  • investigate whether any two rectangles, or any two isosceles triangles, are similar (Problem Solving) CCT
  • match the sides and angles of similar figures CCT
  • name the vertices in matching order when using the symbol ||| in a similarity statement L
  • use the enlargement transformation and measurement to determine that the size of matching angles and the ratio of matching sides are preserved in similar figures CCT
  • use dynamic geometry software to investigate the properties of similar figures (Problem Solving) ICTCCT
  • Solve problems using ratio and scale factors in similar figures (ACMMG221)
  • choose an appropriate scale in order to enlarge or reduce a diagram
  • enlarge diagrams such as cartoons and pictures (Reasoning)
  • construct scale drawings
  • investigate different methods for producing scale drawings, including the use of digital technologies (Communicating, Problem Solving) ICTCCT
  • interpret and use scales in photographs, plans and drawings found in the media and in other key learning areas CCT
  • determine the scale factor for pairs of similar polygons and circles
  • apply the scale factor to find unknown sides in similar triangles
  • calculate unknown sides in a pair of similar triangles using a proportion statement
  • apply the scale factor to find unknown lengths in similar figures in a variety of practical situations
  • apply the scale factor to find lengths in the environment where it is impractical to measure directly, eg heights of trees, buildings (Problem Solving) CCT

Background Information

The definitions of the trigonometric ratios depend upon the similarity of triangles, eg any two right-angled triangles in which another angle is the same, say 30°, must be similar.