Okay Thanks! What I meant by 'how many proofs for each' was similar triangles, congruent triangles, alternate etc
These can be found in any textbook. They stem down from properties of the geometric figure we're interested in.
Parallel lines have corresponding angles equal, alternate angles equal and cointerior angles corresponding,
Hence, if one of the following are true:
1. If alternate angles equal
2. If corresponding angles equal
3. If cointerior angles add to 180deg
Then they are parallel
Congruent triangles look the exact same, so they must have the exact same sides and angles.
Therefore
1. SSS works because you just showed all 3 sides match up
2. SAS works because imagine you have two lines equal in size. Join them together. The only thing you can change is the angle. If you fix that angle, you're stuck.
3. AAS works because imagine you have two angles. If two angles are equal, the third is equal because a triangle only has three angles. So what can you do? Make the triangle larger or smaller. If you fix a side, you end up fixing all three sides.
4. RHS - a special case, and only works because right angled triangles are nice