• Mathematics
  • Year 10

Properties of Geometrical Figures

approx. 10 hrs

8 topics

23 concepts

Develop an aptitude for Properties of Geometrical Figures and advance into Year 11 with confidence.

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Year 10 Properties of Geometrical Figures is aligned to the Australian Mathematics curriculum. This topic builds on prior knowledge and understanding of congruent and similar figures from previous years. Students studying Year 10 Properties of Geometrical Figures select appropriate tests for congruence or similarity to find unknown angles and sides of 2D shapes and to prove geometrical properties of quadrilaterals.

Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 23 concepts.

  • Review Angle Relationships 2 concepts

    1. Use angle relationships to identify parallel lines

    2. Use angle relationships of parallel lines to find the size of unknown angles, giving reasons

  • Review Triangle Relationships 3 concepts

    1. Classify triangles according to side and angle properties

    2. Investigate and apply the exterior angle of a triangle property to find angles in a given diagram

    3. Investigate and use the angle sum of a triangle property to find angles in a given diagram

  • Review Quadrilateral Relationships 2 concepts

    1. Classify special quadrilaterals on the basis of their properties

    2. Use the angle sum of a quadrilateral property to find angles in a given diagram

  • Review Polygons 2 concepts

    1. Apply Exterior Angle Sum of Polygons

    2. Apply the Interior Angle Sum of a Polygon formula

  • Review Congruency 3 concepts

    1. Investigate the minimum conditions needed for two triangles to be congruent

    2. Apply properties of congruent triangles to find an unknown angle or side, giving reasons

    3. Choosing a test for congruence (SSS test, SAS test, AAS test, RHS test)

  • Formal Proofs of Congruence 3 concepts

    1. Use congruence to test for a type of quadrilateral

    2. Application of congruent triangles to prove properties of special triangles and quadrilaterals

    3. Write formal proofs of congruence of triangles, preserving matching order of vertices

  • Review Similarity 4 concepts

    1. Investigate the minimum conditions needed for two triangles to be similar

    2. Determine the scale factor of two similar figures

    3. Use a scale factor to find unknown sides

    4. Solve problems using ratio and scale factors in similar figures

  • Formal Proofs of Similarity 4 concepts

    1. Prove and apply theorems and properties related to triangles and quadrilaterals using congruency and similarity results

    2. Write formal proofs of similarity of triangles, preserving matching order of vertices

    3. Scaling ratio for area

    4. Tests for similar triangles

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Properties of Geometrical Figures


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

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