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Side Splitter TheoremA 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.
Corollary to Side Splitter Related: What are Similar Triangles | Theorems proving Similar Triangles| geometric mean | Side Splitter Theorem | Angle Bisector Theorem |Area & Similarity
Illustrated Example Two
The Side Splitter theorem states that 
Illustrated Example Two
By the side splitter theorem, we know that
the AB / BD = the AC / CE Corollary to Side Splitter Related: What are Similar Triangles | Theorems proving Similar Triangles| geometric mean | Side Splitter Theorem | Angle Bisector Theorem |Area & Similarity
Problem 1)
Find the length of VX by using the side splitter theorem.
Side VX
To solve this problem, set up the following proportion and solve: VW/WY = VX/XZ Corollary to Side Splitter Related: What are Similar Triangles | Theorems proving Similar Triangles| geometric mean | Side Splitter Theorem | Angle Bisector Theorem |Area & Similarity 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.
Practice Problem 1)Use the corollary to find the value of x in the problem pictured below.
Answer 
Practice Problem 2)
Use the corollary to find the value of x in the problem pictured below.
Answer 
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