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Question
In the given figure, PQRS is a parallelogram in which PA = AB = Prove that: SA ‖ QB and SA = QB.
Solution
Construction:
Join BS and AQ.
Join diagonal QS.
Since diagonals of a parallelogram bisect each other.
∴ OP = OR and OQ = OS
Also, PA = AB = BR
Now, OP = OR and PA = PB
⇒ OP - PA = OR - PB
⇒ OA = OB
Thus, in quadrilateral SAQB, we have
OQ = OS and OA = OB
⇒ Diagonals of a quadrilateral SAQB bisect each other.
⇒ SAQB is a parallelogram.
⇒ SA || QB
⇒SA = QB. ...(Opposite sides are equal)
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