Question

Prove that the diagonals of a parallelogram bisect each other.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Your Question :

Prove that the diagonals of a parallelogram bisect each other.

Given :

ABCD is a parallelogram, in which AB || DC and AD || BC, and the diagonals AC and BD intersect at the point O.

To Prove :

• OA = OC and OB = OD

Proof :

In ∆OAB and ∆OCD,

➻ ∠OAB = ∠OCD ㅤㅤ(∵ AB || DC and alternate angles are equal)

➻ AB = DC ㅤㅤ (∵ opposite sides of a parallelogram are equal)

and ∠OBA = ∠ODC ㅤㅤ(AB || DC and alternate angles are equal)

➯ ∆OAB ≅ ∆OCD ㅤㅤ(A-S-A conditions of congruence)

So, the corresponding sides of ∆OAB and ∆OCD are equal.

∴ OA = OC and OB = OD. ㅤㅤ[Proved]

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