If `ABCD` is a quadrilateral such that `AB` `=` `AD` and `CB` `=` `CD` , then prove that `AC` is the perpendicular bisector of `BD`.

Explanation

To prove that line segment AC is the perpendicular bisector of line segment BD in quadrilateral ABCD, given that AB = AD and CB = CD, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Information:**
We are given that AB = AD and CB = CD in quadrilateral ABCD.

2. **Consider Triangles ABC and ADC:**
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