Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Question

aum · Answer

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aum · Answer

DE is parallel to BC.
Triangles ADE and ABC are similar because angle A is shared by both triangles and angle ADE = angle ABC (corresponding angles).  So by the two angles postulate, ADE and ABC are similar.  
AB / AD = AC / AE  
(AD+DB) / AD = (AE + EC) / AE
1 + DB / AD = 1 + EC / AE
subtract 1:
DB / AD = EC / AE

Thus, a line parallel to one side of a triangle divides the other two sides proportionally.