Congruent triangles
Same size + shape. Four valid tests.
Congruent = identical (one fits exactly on the other).
Four valid congruence tests:
| Test | What's needed |
|---|---|
| SSS | Three corresponding sides equal |
| SAS | Two sides and the INCLUDED angle equal |
| ASA | Two angles and one corresponding side equal |
| RHS | Right-angle, Hypotenuse, one Side equal (right-angled only) |
NOT a valid test: SSA (ambiguous — could give two different triangles).
Important. For SAS, the angle must be BETWEEN the two sides. SSA (where angle is NOT between) doesn't always work.
Worked qualitative. Why isn't SSA a valid test?
- Two triangles can share two sides and a non-included angle, but be different triangles.
- Example: with two sides and angle NOT between them, you can construct two distinct triangles.
- This is the 'ambiguous case' from the sine rule.
Edexcel tip. State the test name (SSS, SAS, etc.) explicitly when proving congruence. Mark schemes give M1 for naming, A1 for justification.
- SSS, SAS, ASA, RHS.
- SAS: angle BETWEEN sides.
- RHS for right-angled triangles.
- SSA NOT valid.