Question

if the diagonal of parallelogram bisect each other then the quadrilateral is a parallelogarm​

Answer 1

HELLO BUDDY!!

Given: A quadrilateral ABCD whose diagonals AC and BD bisect each other at point O. i.e., OA = OC and OB = OD

To prove: ABCD is a parallelogram i.e., AB ║ DC and AD ║ BC.

Proof: In ∆AOB and ∆COD

OA = OC [Given]

OB = OD [Given}

∠AOB = ∠COD [Vertically opposite angles]

⇒ ∆AOB ≅ ∆COD [By SAS] ⇒ ∠1 = ∠2 [By cpctc]

But these are alternate angles and whenever alternate angles are equal, the lines are parallel.

∴ AB is parallel to DC i.e., AB ║ DC Similarly, ∆AOD ≅ ∆COB [By SAS]

⇒ ∠3 = ∠4 But these are also alternate angles ⇒ AD ║ BC AB ║ DC and AD ║ BC

⇒ ABCD is a parallelogram.

Answer 2

Answer:

please mark it as Brainliest:-