# Side Splitter Theorem

## 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:

1. The side splitter theorem tells us that ACCE = ABBD.
2. We need the length of segment CE before we can solve for BD.
AC + CE = AE
5 + CE = 7
CE = 2
3. Now, let's evaluate the ratio ACCE.
ACCE = 52
4. We can now apply the side splitter theorem to find the length of BD.
ACCE = ABBD
52 = 3BD
BD = 65
5. Segment BD is 65 long.
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