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
• 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 right-angled triangles in which another angle is the same, say 30°, must be similar.