We are given the following information:

• The length of segment $AD = 25$ units.
• The length of segment $AC = 19$ units.
• The length of segment $BD = 14$ units.

We need to determine the length of segment $BC$.

Steps to solve:

1. Determine the length of $CD$: From the diagram, we know that $D$ is the endpoint, so: $CD = BD - BC$

2. Relating segments: Since $AD = AC + CD$, we can express $CD$ as: $CD = AD - AC = 25 - 19 = 6$

3. Determine $BC$: Since $BD = BC + CD$, we now know $CD = 6$, so: $BD = BC + CD = BC + 6$ Substituting the value of $BD = 14$: $14 = BC + 6$ Solving for $BC$: $BC = 14 - 6 = 8$

Thus, the length of segment $BC$ is $\boxed{8}$ units.

Would you like any further clarification on this solution?

Related Questions:

1. If segment $AB$ was 13 units, how would you solve for the length of $BC$?
2. What would be the length of $BC$ if $AD = 30$ units and $BD = 16$ units?
3. How does the subtraction method work for solving similar problems in geometry?
4. If the points $B$ and $C$ are equidistant, what would be the length of $AB$ and $CD$?
5. Can you apply this method to a problem involving three dimensions?

Tip: Always sketch the diagram with labeled points and known values when solving geometric segment problems to keep track of relationships between parts.