Two Equidecomposable Triangles
This Demonstration shows a dissection of two triangles with the same area and altitude into the same set of pieces, using the fact that both can be dissected into a rectangle with area and altitude .
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.
 G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 1997 p. 139. www.cs.purdue.edu/homes/gnf/book.html.