Question

Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE⎯⎯⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯⎯⎯⎯AE¯≅EC¯ and BE⎯⎯⎯⎯⎯⎯⎯≅DE⎯⎯⎯⎯⎯⎯⎯⎯BE¯≅DE¯. Can you prove can you prove that the figure is a parallelogram? Explain.

Answer 1

Given:

In a quadrilateral ABCD, diagonals AC and BD intersect at point E.

$AE\cong EC$

$BE\cong DE$

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.

$AE\cong EC$

$BE\cong DE$

Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.

Hence proved.