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K–10Mathematics K–10 Syllabus

Record of changes
Implementation for K–2 from 2023 and 3–10 from 2024
Expand for detailed implementation advice

Content

Stage 5

Properties of geometrical figures B (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Identify and explain congruence
  • Identify figures as Loading  figures if Loading , Loading  and rotations can move one figure exactly on top of another

  • Match the Loading  and Loading  of 2 congruent Loading 

  • Indicate 2 polygons are congruent using the symbol () and name the vertices in matching order

  • Determine that having equal radii is the condition for 2 Loading  to be congruent

Develop and use the conditions for congruent triangles
  • Establish the 4 congruence tests for Loading  (SSS, SAS, AAS and RHS)

  • Use the congruence tests to identify a pair of congruent triangles from a selection of 2 or more triangles

Develop and apply the minimum conditions for triangles to be similar
  • Examine the minimum conditions needed and establish the 4 tests for 2 triangles to be similar

  • Apply the minimum conditions needed and determine whether 2 triangles are similar using an appropriate test

Establish and apply properties of similar shapes and solids
  • Establish for 2 similar figures with similarity ratio a:b that their areas are in the ratio a2:b2 and their volumes are in the ratio a3:b3

  • Solve problems involving areas and Loading  of similar Loading  and solids

Apply logical reasoning to numerical problems involving plane shapes
  • Apply geometrical facts, properties and relationships to find the sizes of unknown sides and angles of plane shapes in diagrams, providing appropriate reasons

  • Define the exterior angle of a convex polygon

  • Establish the sum of the exterior angles of any convex polygon is 360° and verify this result

  • Apply the result for the sum of the Loading  of a triangle to find, by dissection, the sum of the interior angles of a polygon with more than 3 sides

  • Apply the results for the interior and exterior angles of polygons to solve problems involving polygons

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