Year 8 Mathematics · AC9M8SP01

Congruence and Similarity of Shapes

Congruent shapes match exactly; similar shapes preserve corresponding angles and scale every corresponding length by one common factor. Use valid conditions…

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Key conceptTeach from the board

Congruent means same shape and same size. A translation, rotation or reflection can move one congruent shape exactly onto another without changing lengths or angles.

Similar means same shape but not necessarily same size. Corresponding angles are equal and all corresponding side lengths share one scale factor. Enlargement is the key transformation that produces similar shapes.

For triangles, sufficient congruence conditions include SSS, SAS, ASA/AAS and RHS. Similarity can be established by equal corresponding angles (AAA) or proportional corresponding sides with the required angle information. A condition must be sufficient; appearance is never evidence.

Preserve the full AC9 intent by testing transformations, logical conditions, correspondence and counterexamples. A false rule should fail when a carefully chosen example meets the proposed condition but not the conclusion.

Worked examplesWe do

Worked examples

AC9M8SP01 - Congruence and Similarity of Shapes
Example 1

Classify two identical triangles in different orientations as congruent/similar/both.

Example 2

Decide whether given SSS information is sufficient for congruence.

Example 3

Identify corresponding sides in a pair of similar triangles.

Example 4

State what changes and what stays invariant under an enlargement of scale factor 1.5.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8SP01: identify the conditions for congruence and similarity of triangles and explain conditions for other common shapes, including those formed by transformations.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8SP01:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-GEO-C-01; MAO-WM-01:Partial. Stage 4 develops triangle/quadrilateral properties and congruence reasoning; the national descriptor’s full similarity-condition emphasis is broader than one Stage 4 outcome.

LessonAC v9VictoriaNSW
Congruence and similarity conditionsAC9M8SP01VC2M8SP01 — ExactMA4-GEO-C-01; MAO-WM-01 — Partial
Questions and answersWith answers
  1. What is congruence? Same shape and same size, with equal corresponding lengths and angles.
  2. What is similarity? Equal corresponding angles and one common scale factor for corresponding lengths.
  3. Why does correspondence order matter? It ensures the correct sides and angles are compared.
  4. What do rigid transformations preserve? Lengths, angle sizes, shape and therefore congruence.
Practice and reviewReady for practice
  • Same angles means congruent. Equal angles establish shape, not size; AAA proves similarity only.
  • Any three pieces of data prove congruence. The information must match a sufficient condition such as SSS, SAS, ASA/AAS or RHS.
  • Correspondence follows visual position. Match vertices by equal angles and side relationships, not left/right placement.
  • Enlargement preserves congruence. Unless scale factor is 1, enlargement changes lengths and gives similarity rather than congruence.
Curriculum alignmentStart here
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