Given:
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
To prove:
The figure is a parallelogram.
Solution:
We know that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.
Hence proved.
