In proposition 24 (1.24) of Elements, Euclid uses proposition 4 (1.4) to demonstrate triangle equality before going on to finish the proof. However, before he uses 1.4, he uses proposition 23 (1.23) to replicate an angle of one of the given triangles. But in 1.23, in order to replicate an angle, we first replicate a triangle, and then because we know two equal triangles are equal in every way, we know that the angle we were trying to replicate is, in fact, replicated.
So my question is: why do we use 1.4 to show triangle equality, rather than just acknowledge that in order to replicate an angle we first build a triangle equal to another triangle that contains an angle that we want to replicate? Put another way: isn't the fact of triangle equality implied by the use of 1.23?
