Test triangle congruence
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 has sides 3,4,5 cm; triangle B has sides 5,3,4 cm. Triangle C has sides 6,8,10 cm.
Congruent triangles have the same size and shape; matching side lengths and angles must correspond in the same order. SSS and SAS are sufficient tests. AAA establishes shape but not size.
Test triangle congruence — worked practice
Congruent triangles have the same size and shape; matching side lengths and angles must correspond in the same order. SSS and SAS are sufficient tests. AAA establishes shape but not size.
Case: triangle A has sides 3,4,5 cm; triangle B has sides 5,3,4 cm. Triangle C has sides 6,8,10 cm.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Case: triangle A has sides 3,4,5 cm; triangle B has sides 5,3,4 cm. Triangle C has sides 6,8,10 cm. |
Copy as plain text
1. 1. Match
Pair equal side lengths of A and B.
You should see: 3↔3,4↔4,5↔5.
2. 2. Test
Apply the SSS criterion.
You should see: A and B are congruent.
3. 3. Compare
Check A against C.
You should see: Every C side is twice A; they are not congruent.
4. 4. Distinguish
Explain what matching angles alone establishes.
You should see: Same shape can have different size; AAA alone is insufficient for congruence.
What to finish
A congruence comparison distinguishing equal size from equal shape.
Watch for this
Scaling preserves shape and angles while changing lengths.
How can I tell I understand it?
Distinguish SSS or SAS evidence from angle-only similarity.
Quick knowledge check
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Source & access notes · checked 2026-10-01
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