Elements I.42
To construct a parallelogram equal to a given triangle in a given rectilinear angle
Let E be the midpoint of BC. Construct an angle congruent to on the ray EC, on the side of A.
Draw the parallel to BC passing by A, and let F be the point of the intersection of this line with the angle just constructed.
Draw the parallel to EF passing by C and let G be its point of intersection with AF.