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Side Splitter Theorem

A theorem to find sides of similar triangles

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
Side Splitter Theorem Picture The Side Splitter theorem states that $ \frac{AC}{CE} = \frac{AB}{BD} $




Is the proportion below true?

formula non example
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
corollary to side splitter theorem example, picture
Example 2
Side Splitter full
Practice Problems


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

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

problem on corollary to side splitter theorem

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

problem on corollary to side splitter theorem

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