Enter the length of lines A to C, C to E, and A to B from the diagram into the calculator to determine the length of B to D using the side-splitter theorem.

Side Splitter Theorem Formula

The following formula is used to calculate the missing length of a triangle that has been split by a line parallel to its base.

AC / CE = AB / BD

CE = AC * BD / AB

  • Where AC , CE, AB, and BD are the point to point lengths shown on the triangle below.

What is the side splitter theorem?

Definition:

The side splitter theorem is a mathematical property in geometry that says 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.

How to calculate side splitter theorem?

Example:

The following example shows the steps and information needed to calculate the missing length of a triangle that has been split.

First, determine the length A to B in the triangle above. For this example, the length is found to be 5.

Next, determine the length B to D. In this case, that length is 4.

Next, determine the length A to C. For this problem, that is measured to be 3.

Finally, calculate the missing length C to E using the formula above:

CE = AC * BD / AB

CE = 3 * 4 / 5

CE = 2.4