Details

The first to give a dissection of a non-equilateral triangle to a different non-equilateral triangle was Henry Taylor (1905). Lindgren (1953) observed that Taylor's dissection could be constructed using triangular strips. Namely, two copies of a triangle form a parallelogram, and copies of the parallelogram form a parallelogram (P) strip. Two P-strips intersect in a parallelogram and half of it determines triangle dissection.

Reference

[1] G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 1997 p. 139. www.cs.purdue.edu/homes/gnf/book.html.