Recommended first: Transformations. You can still continue here.
Congruent triangles are exact copies. You don't need to check all six parts. Certain combinations of three are enough to lock the triangle in place.
| Rule | What matches |
|---|---|
| SSS | All three sides |
| SAS | Two sides and the angle between |
| ASA | Two angles and the side between |
| AAS | Two angles and a side not between |
| HL | Hypotenuse and leg of right triangles |
Work through it
Two triangles share sides of 5 and 7, with a angle between them in both. Are they congruent?
The angle is between the sides.SAS
So yes.Congruent
Two triangles have angles . Are they congruent?
Equal angles only give the same shape.Similar
One could be bigger.Not proven
Watch out for this
Using SSA.
Two sides and a non-included angle can make two different triangles.
The short version
Use SSS, SAS, ASA, AAS or HL. SSA and AAA don't prove congruence.
Use SSS, SAS, ASA, AAS or HL. SSA and AAA don't prove congruence.
Your turn
Prefer paper? Print the Coordinate geometry and transformations worksheet, with an answer key.
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