I'm currently wondering about the side splitter theorem.
Lets say I have this triangle. Now the side splitter theorem says, that if a line is parallel to a side of a triangle and intersects the two other sides, then this line divides those two sides proportionally.
In my triangle, MB is parallel to CD and intersects EC and ED.
So the theorem states that: $\frac{EB}{BD} = \frac{EM}{MC}$.
I'm wondering if the following equation is also possible: $\frac{MB}{CD} = \frac{EM}{EC}$. This equation is used in some methods of computer science (calculate corresponding screen positions), but I'm not sure, why and in which case it is correct. Does it only work because of the right angle at C ?
Thanks
$\endgroup$ 31 Answer
$\begingroup$Triangles $ EMB $ and $ CDE $ are similiar, so yes, the last relation you mentioned holds.
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