Geometry

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# Side Splitter Theorem

#### Lesson Contents

## 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.**

### 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 ^{AC}⁄_{CE} = ^{AB}⁄_{BD}.

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 ^{AC}⁄_{CE}.^{AC}⁄_{CE} = ^{5}⁄_{2}

4.) 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}

5.) **Segment BD is ^{6}⁄_{5} long.**

Result :

Worksheet 1

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Cheat sheet

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