little_dragon wrote:My book showed lots of ways you can know two triangles are congruent, like SSS, SAS, RHS. In SAS, it is true that you
have to have the A in the middle so the same-size angles are between the same-size sides? My mother said that otherwise you'd have "A$$", which is a way of remembering that you shouldn't do it that way, but that sounds made-up.
Yes, the angle
must be between the two given sides (SAS), as with ASS / SSA, there may be 0, 1, or 2 possible triangles that could be drawn, depending on the dimensions of the known sides and angle.
The RHS / HL rule is actually a special case of ASS / SSA, but that only works because the right angle forces there to be only one possible solution. Any other angle instead of the right angle would either result in two possible solutions (if the remaining side is longer than the minimum length needed to close up the triangle), or no possible solution (if the remaining side would be shorter than the minimum length needed to close up the triangle).
Here are some
diagrams which will hopefully make things clearer. (Scroll down to the picture of a donkey / ass.)
DAiv