#### 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, and it happens any time that a pair of parallel lines intersect a triangle.

Example
The Side Splitter theorem states that

$
\frac{AC}{CE} = \frac{AB}{BD}
$

#### Is the proportion below true?

**No**, this example is not accurate. PM is obviously not parallel to OM

Therefore, the side splitter theorem does **not ** hold and is not true.

#### Is the proportion below true?

**No**, remember this theorem only applies to the segments that are 'split' or intercepted by the parallel lines.

Instead, you could set up the following proportion:

$ \frac{VW}{WY} = \frac{VX}{XZ} $