If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Let the triangles a b c and d e f have the side a b of the one equal to the side d e of the other; the side a c of the one equal to the side d f of the other; and the included angle b a c of the one equal to the included angle e d f of the other, each to each; then will the two triangles be equal in all their parts.
For, place the triangle d e f upon the triangle a b c, so that the line d e shall fall upon the line a b, with the point d upon the point a.
Because the line d e is equal to the line a b, the point e will fall upon the point b.
Because the angle e d f is equal to the angle b a c, the line d f will fall upon the line a c.
Because the line d f is equal to the line a c, the point f will fall upon the point c.
Then, because the point e is on the point b, and the point f on the point c, the line e f will coincide with the line b c, and the two triangles will be found equal in all their parts;
That is, the angle e is found to be equal to the angle b, the angle f to the angle c, the line e f to the line b c, and the area of the triangle a b c to the area of the triangle d e f.
