In `Delta ABC, AB lt AC`. Then, ........ holds good

Options

A. `angleA lt angle B`
B. `angleB lt angle C`
C. `angleC lt angle A`
D. `angleC lt angle B`

Answer

To solve the problem, we need to analyze the relationship between the sides and angles of triangle ABC given that \( AB < AC \).

### Step-by-Step Solution:

1. **Identify the Given Information**:
We are given a triangle ABC where \( AB < AC \).

2. **Understand the Relationship**:
In any triangle, the sides are directly related to the angles opposite to them. Specifically, if one side is shorter than another, the angle opposite the shorter side is also smaller than the angle opposite the longer side.

3. **Apply the Triangle Inequality Theorem**:
Since \( AB < AC \), we can conclude that the angle opposite side AB (which is angle C) is less than the angle opposite side AC (which is angle B). Therefore, we can write:
\[ \angle C < \angle B \]

4. **Conclude the Result**:
Thus, the relationship that holds true in triangle ABC is:
\[ \text{If } AB < AC, \text{ then } \angle C < \angle B. \]

### Final Answer:
The statement that holds good is: **If \( AB < AC \), then \( \angle C < \angle B \)**.

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