All the triangles are similar in the diagram above. What is interesting about it is that

or in terms of the dotted / solid parallelograms:

**Derivation**

(1) The ratio of area of A1 to A2 is

……subscripts correspond to triangle depicted above

(2) The ratio of area A3 to A2 is:

(3) Base of the big overall triangle:

(4) Substitute #3 into #2

(5) Expand right side

(6) The area of the overall big triangle also is related as follows

(7) Substituting #6 in #5:

(8) referring back to #1 we can cancel the term on both sides of the equation. The one also cancels on both sides leaving:

(9) Moving terms around:

(10) #1 can be rearranged to

(11) Cutting a term out of #9 equal to #10 yields

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