Question

prove that that the diagonal of a parallelogram bisect each other.

Answer 1

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We have to prove that the diagonals bisect each other in a parallelogram ABCD.

∠ABE≃∠CDE ( by alternate interior angles )

∠DEC≃∠BAE ( alternate interior angles )

∠ABE≃∠CDE by ASA

⇒{AE=CEBE=CE} coordinate sides of ≅ triangle

∠CED≅∠BEA [ vertical angles ]

△AEB≅△DEC [ by SAS≅A ′ s ]

∠CDE≅∠BAE [ coordinate angles of ≅ triangles. ]

∴AB∥CD by alternate interior angles ≅ of parallel lines.

∠AEC≅∠DEB ( vertical angles )

△AEC≅△DEB ( by SAS )

∠CAE≅∠BDE [ coordinate angle ]

∴AC∥BC by alternate interior angles

Theorm :

Theorm :A quadrilateral is a parallelogram if and only if the diagonals bisect each other.

Answer 2

Step-by-step explanation:

Hence Proved

I hope it helps