4. M and N are points on opposite sides AD and BC of a parallelogram
ABCD such that MN passes through the point of intersection O of its
diagonals AC and BD. Show that MN is bisected at O.
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Answer:
Consider △AOM and △CON
From the figure we know that ∠MAO and ∠OCN are alternate angles
∠MAO=∠OCN
we know that the diagonals of parallelogram bisect each other
AO=OC
∠AOM and ∠CON are vertically opposite angles
∠AOM=∠CON
By ASA congruence criterion
△AOM≅△CON
MO=NO (c.p.c.t)
therefore, it is proved that MN is bisected at O.
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