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# Side Splitter Theorem

## What is the side splitter theorem?

Answer:
The side splitter theorem states that if a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.
The side splitter theorem is a natural extension of similarity ratio.
Example
 The Side Splitter theorem states that $\frac{AC}{CE} = \frac{AB}{BD}$

## Is the proportion below true?

 Answer
$\frac{LP}{PO} = \frac{LM}{MN}$

## Is the proportion below true?

 Answer
$\frac{VW}{WY} = \frac{WX}{YZ}$

## What if there are more than two parallel lines?

Answer: A corollary of the this theorem is that when three prallel lines intersect two transversals, then the segments intercepted on the transversal are proportional.
Example
Example 2
Practice Problems

Problem 1) Find the length of VX by using the side splitter theorem.
 Answer

Problem 2) Use the corollary to find the value of x in the problem pictured below.
 Answer

Problem 3) Use the corollary to find the value of x in the problem pictured below.
 Answer

Problem 4) Are the red segments pictured below parallel? (Picture not to scale)
 Answer