Parallel Lines and Similar Triangles:
What is it about?
A Mathematical Droodle
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Copyright © 1996-2018 Alexander Bogomolny
The problem is: in ΔABC draw lines BD and CE with D on AC and E on AB. Let F on AB and G on AC be such that DF||CE and EG||BD. Then FG||BC.
Let K be the intersection of DF and EG.
We may detect several pairs of similar triangles and derive several proportions. We need just two. Since triangles ABD and AEG,
AE/AB = AG/AD.
Since triangles ACE and ADF are similar, we have also
AF/AE = AD/AC.