Use similarity without guessing
See this course’s project requirements
A geometry explanation board with angle deductions, congruence and similarity tests, a scale argument and a checked space-design decision.
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What to include
- Keep every given and correspondence visible.
- Show angle deductions with their reasons.
- Distinguish congruence from similarity.
- Check length, area and volume scale factors.
- Write a final panel explanation and all changed-case responses.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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The idea in everyday life
Case: triangle A sides 4,6,8 cm; triangle B corresponding sides 6,9,12 cm.
Similar shapes have equal corresponding angles and one consistent length scale factor. Name correspondences before dividing. A convenient single ratio does not prove every side matches.
Use similarity without guessing — worked practice
Similar shapes have equal corresponding angles and one consistent length scale factor. Name correspondences before dividing. A convenient single ratio does not prove every side matches.
Case: triangle A sides 4,6,8 cm; triangle B corresponding sides 6,9,12 cm.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Case: triangle A sides 4,6,8 cm; triangle B corresponding sides 6,9,12 cm. |
Copy as plain text
1. 1. Compare
Calculate B/A for each corresponding length.
You should see: 6/4=9/6=12/8=1.5.
2. 2. Classify
Use the common factor.
You should see: These corresponding side triples are similar.
3. 3. Predict
Apply factor 1.5 to another corresponding segment 2 cm.
You should see: Its matching segment is 3 cm.
4. 4. Reject
Check a changed B side set 6,10,12.
You should see: 10/6 differs from 1.5; consistent SSS similarity is not established.
What to finish
A similarity test, corresponding-length prediction and rejected mismatch.
Watch for this
Similarity requires consistent correspondence.
How can I tell I understand it?
Reject a convenient isolated ratio when other corresponding sides do not agree.
Quick knowledge check
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Source & access notes · checked 2026-10-01
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