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Question
PQRS is a parallelogram. L and M are points on PQ and SR respectively such that PL = MR.
Show that LM and QS bisect each other.
Solution
Given: PL = MR ...(i)
To prove SR = PQ ...(ii) (parallelogram opposite sides)
SP - PQ and SR - MR
LQ = SM ...(iii)
In ΔLOQ & ΔMOS
∠LQO = ∠MSO ....( alternate interior angles )
∠OLQ = ∠OMS ....( alternate interior angles )
LQ = SM ...(from (iii))
ΔLOQ ≅ ∠MSO ...(by ASA congruence)
Then, OL = OM
OQ = OS ...(by c.p.c.t.c)
Hence, LM and QS bisect each other.
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