`ABCD` is a quadrilateral in which `AB=BC` and `AD =CD` ,Show that `BD` bisects both the `angle ABC` and `angle ADC`.

Explanation

To prove that line segment \( BD \) bisects both angles \( \angle ABC \) and \( \angle ADC \) in quadrilateral \( ABCD \) where \( AB = BC \) and \( AD = CD \), we will use the concept of congruent triangles.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We are given a quadrilateral \( ABCD \) where \( AB = BC \) and \( AD = CD \).

2. **Draw the Quadrilateral:**
...