Question

to prove that diagonals of a parallelogram. bisect each other complete the following proof. give me answer proof :∆POS and ∆ROQ.​

Answer 1

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Answer 2

To Prove :- The diagonals of a parallelogram bisect each other .

Answer :-

from image we have,

• PQRS is a parallelogram .
• Diagonals PR and QS meets at O .

Proof :-

In ∆POS and ∆ROQ we have,

→ ∠OPS = ∠ORQ (since opposite sides of a parallelogram are parallel , PS || QR , so, alternate interior angles.)

→ PS = RQ (Opposite sides of parallelogram are equal.)

→ ∠OSP = ∠OQR (Alternate interior angles.)

so,

→ ∆POS ≅ ∆ROQ (By ASA.)

then,

→ PO = RO and SO = QO (By CPCT.)

Therefore, we can conclude that, the diagonals of a parallelogram bisect each other.

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