Outcomes
A student:

 MA5.11WM
uses appropriate terminology, diagrams and symbols in mathematical contexts

 MA5.12WM
selects and uses appropriate strategies to solve problems

 MA5.13WM
provides reasoning to support conclusions that are appropriate to the context

 MA5.111MG
describes and applies the properties of similar figures and scale drawings
Related Life Skills outcomes: MALS32MG, MALS33MG, MALS34MG
Content
 Students:
 Use the enlargement transformation to explain similarity (ACMMG220)
 describe two figures as similar if an enlargement of one is congruent to the other
 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)
 explain why any two equilateral triangles, or any two squares, are similar, and explain when they are congruent (Communicating, Reasoning)
 investigate whether any two rectangles, or any two isosceles triangles, are similar (Problem Solving)
 match the sides and angles of similar figures
 name the vertices in matching order when using the symbol  in a similarity statement
 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
 use dynamic geometry software to investigate the properties of similar figures (Problem Solving)
 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)
 interpret and use scales in photographs, plans and drawings found in the media and in other key learning areas
 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)
Background Information
The definitions of the trigonometric ratios depend upon the similarity of triangles, eg any two rightangled triangles in which another angle is the same, say 30°, must be similar.