Which of the following is true for `DeltaABC`   ?

Options

A. `AB-BCgtAC`
B. `AB+BCltAC`
C. `AB-BCltAC`
D. `AB+ACltBC`

Answer

To determine which statement is true for triangle ABC, we can analyze the properties of triangles.

### Step-by-Step Solution:

1. **Understanding Triangle Properties**:
In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

2. **Identify the Sides**:
Let's denote the sides of triangle ABC as follows:
- AB = a
- BC = b
- AC = c

3. **Applying the Triangle Inequality Theorem**:
According to the theorem, the following inequalities must hold true:
- a + b > c (sum of sides AB and BC is greater than side AC)
- a + c > b (sum of sides AB and AC is greater than side BC)
- b + c > a (sum of sides BC and AC is greater than side AB)

4. **Analyzing the Given Statements**:
We need to evaluate the statements provided in the question. One of the statements might involve comparing the differences between the sides, such as:
- AB - BC > AC
- AB - BC < AC
- etc.

5. **Evaluating the Statements**:
If we consider the statement "AB - BC < AC", we can analyze it:
- If AB is less than BC, then subtracting BC from AB will yield a negative number, which is certainly less than AC if AC is a positive length.
- This aligns with the triangle inequality, as it supports the idea that the difference between two sides must be less than the third side.

6. **Conclusion**:
Based on the triangle inequality properties, we can conclude that the statement "AB - BC < AC" is true for triangle ABC.

### Final Answer:
The true statement for triangle ABC is: **AB - BC < AC**.