## Side Splitter Theorem Lesson

### What is the Side Splitter Theorem?

The side splitter theorem applies to all triangles. It tells us that:

**If a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides into proportional segments.**

INTRODUCING

### Side Splitter Theorem Example Problem

Triangle *ADE* in the image above is intersected by line *BC*. Line *BC* is parallel to side *DE*. If side *AE* is 7 long, segment *AC* is 5 long, and segment *AB* is 3 long, what is the length of segment *BD*?

Solution:

- The side splitter theorem tells us that
^{AC}⁄_{CE}=^{AB}⁄_{BD}. - We need the length of segment
*CE*before we can solve for*BD*.*AC*+*CE*=*AE*

5 +*CE*= 7*CE*= 2 - Now, let's evaluate the ratio
^{AC}⁄_{CE}.^{AC}⁄_{CE}=^{5}⁄_{2} - We can now apply the side splitter theorem to find the length of
*BD*.^{AC}⁄_{CE}=^{AB}⁄_{BD}^{5}⁄_{2}=^{3}⁄_{BD}*BD*=^{6}⁄_{5} **Segment***BD*is^{6}⁄_{5}long.