Step-by-step explanation:
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 :
A quadrilateral is a parallelogram if and only if the diagonals bisect each other.
Hence, the answer proved.
