Side Splitter Theorem Calculator

Formula

To calculate the length CE using the Side Splitter Theorem:

\[ \frac{AC}{CE} = \frac{AB}{BD} \quad \text{or} \quad CE = \frac{AC \cdot BD}{AB} \]

Where:

\(AC\) is the length from point A to point C
\(CE\) is the length from point C to point E
\(AB\) is the length from point A to point B
\(BD\) is the length from point B to point D

What is the Side Splitter Theorem?

The Side Splitter Theorem is a mathematical property in geometry that states the lengths of the sides of a triangle that have been split by a line parallel to the base of the triangle will be directly proportional. This means that if a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally.

Example Calculation

Let's assume the following values:

Length \(AC\) = 10 units
Length \(AB\) = 15 units
Length \(BD\) = 5 units

Using the formula:

\[ CE = \frac{10 \cdot 5}{15} = \frac{50}{15} \approx 3.333 \text{ units} \]

The length \(CE\) is approximately 3.333 units.