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The first to give a dissection of a nonequilateral triangle to a different nonequilateral 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 strip . Two strips intersect in a parallelogram, and half of it determines the 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.