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.
1 answer:
Given:
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
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.
Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.
Hence proved.
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