I only know 3.
SSS (side/side/side) -> if all three sides are the same length
SAS (side/angle/side) -> if two sides and the angle between them are the same
ASA (angle/side/angle) -> if two angles and the side between them are the same
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You can't use AAA to prove two triangles congruent because triangles can have the same measures of all its angles but be bigger or smaller, AAA could probably be used to prove two triangles are similar not congruent.
The basic proportionality theorem is an important tool for proving similarity tests such as SAS. It is used in comparison of similar triangles and finding their measurements.
Excuse me, but two triangles that have A-A-S of one equal respectively to A-A-S of the other are not necessarily congruent. I would love to see that proof!
Yes. Make one triangle using hree matches. Underneath the two vertices at the base of this triangle, make another two triangles, using six more matches. You will find that there is an inverted triangle in the middle - the fourth.
marks used on a figure to indicate congruent