ABC and DBC are two triangle on the same base BC such that A and D lie on the opposite sides of BC,AB=AC and DB =DC ,Show that AD is the perpedicular bisector of BC.

Explanation

To show that line AD is the perpendicular bisector of line segment BC in triangles ABC and DBC, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Information**:
- We have two triangles, ABC and DBC, sharing the same base BC.
- Points A and D lie on opposite sides of line BC.
- It is given that AB = AC and DB = DC.
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