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Side Splitter Theorem

A theorem to find sides of similar triangles

The side splitter theorem is a natural extension of similarity ratio.
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.
Illustrated Example Two
    Side Splitter Theorem Picture

    The Side Splitter theorem states that
Illustrated Example Two

side splitter theorem example By the side splitter theorem, we know that
the AB / BD = the AC / CE

Practice Problems

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

Corrollary to Side Splitter Theorem

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

corollary to side splitter theorem example, picture
Practice Problem 1)Use the corollary to find the value of x in the problem pictured below.
 Answer  

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

problem on corollary to side splitter theorem

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