The line segments joining the midpoints `M` and `N` of parallel sides `AB` and `DC` respectively of a trapezium `ABCD` is perpendicular to both the sides `AB` and `DC`. Prove that `AD`=`BC`.

Explanation

To prove that \( AD = BC \) in trapezium \( ABCD \) where \( M \) and \( N \) are the midpoints of the parallel sides \( AB \) and \( DC \) respectively, and the line segment \( MN \) is perpendicular to both \( AB \) and \( DC \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- \( M \) and \( N \) are the midpoints of sides \( AB \) and \( DC \) respectively.
- \( MN \) is perpendicular to both \( AB \) and \( DC \).

...