If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. GIVEN : A quadrilateral `A B C D` such that its diagonals `A C` and `B D` are such that `a r( A B D)=a r( C D B` ) and `a r( A B C)=a r( A C D)dot` TO PROVE: Quadrilateral `A B C D` is a parallelogram.

Explanation

To prove that the quadrilateral ABCD is a parallelogram given that the diagonals AC and BD divide it into triangles of equal area, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Areas of Triangles:**
We are given that:
\[
\text{Area of } \triangle ABD = \text{Area of } \triangle CDB
...