3.9 Similar shapes and congruence
Use proportional side relationships, scale powers and formal triangle conditions to analyse similarity and congruence.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Identify similar and congruent shapes and find corresponding elements.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Use length, area and volume scale-factor relationships.
Exam cue: Match corresponding sides before forming ratios and state whether the scale factor applies to length, area or volume.
Concept 3
Apply triangle similarity and congruence conditions in calculation and proof.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Treating similarity as congruence or applying a length scale factor unchanged to area and volume.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Similar
Similar shapes have equal corresponding angles and proportional corresponding lengths.
Congruent
Congruent shapes have the same size and shape.
Length scale factor
Corresponding lengths change by k.
Area scale factor
Corresponding areas change by k².
Volume scale factor
Corresponding volumes change by k³.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
If y is directly proportional to x and y=18 at x=6, find y at x=11.
The relation is p∝q², with p=45 when q=3. Find p when q=5.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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