SSS
Three corresponding sides equal.
Learning Objectives
- distinguish similar and congruent figures;
- identify corresponding sides and angles;
- use scale factors in similar figures;
- recognise triangle congruence tests;
- solve missing-length problems.
Introduction
This lesson develops Similarity and Congruence from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Similarity
Similar figures have the same shape but may have different sizes. Corresponding angles are equal and corresponding sides are proportional.
Scale factor = corresponding image length ÷ original length
Congruence
Congruent figures have exactly the same shape and size.
SAS
Two sides and included angle equal.
ASA
Two angles and included side equal.
RHS
Right angle, hypotenuse and one side equal.
Worked Example
Two similar triangles have corresponding sides 6 cm and 15 cm. Scale factor=15÷6=2.5. A corresponding side of 8 cm becomes 20 cm.
Try It: Similar Figures and Scale Factor
| Measure | Original | Image |
|---|---|---|
| Length | 4 cm | 8 cm |
| Area | 12 cm² | 48 cm² |
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
- State one difference between similar and congruent figures.
- Find the scale factor from 4 cm to 10 cm.
- A side of 7 cm is enlarged by factor 3. Find the new length.
- Name the congruence test using two sides and the included angle.
- Similar triangles have side ratio 2:5. A smaller side is 12 cm. Find the corresponding larger side.
✅ Check Your Work
Show answers and working
- Similar figures may differ in size; congruent figures are the same size.
- 2.5.
- 21 cm.
- SAS.
- 30 cm.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Similar: same shape, proportional sides.
- Congruent: same shape and size.
- Use SSS, SAS, ASA or RHS for triangle congruence.