Triangles with 2 sides and inc. angle equal

(Euclid Book 1 Prop 4)

Consider two triangles ABC and PRQ with

       AB = PQ        CB = RQ    ^ABC = ^PQR

If you lay the point Q of triangle PRQ upon point B of triangle ABC and then rotate triangle PRQ until PQ lies upon AB then QR must lie upon BC as ^ABC = ^PQR.

Also the points A and B must lie upon P and R as the lengths of the sides are equal.

Therefore the line PR must lie upon AB as there is only one line between two points.

As all the lines of the triangles lie one upon the other it must follow that the other two angles are equal.

(This proof may not be mathematically rigorous but is sufficient for my own satisfaction.)