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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.

Answer:

Solution

"hello students my name is rabbit singh
and i welcome you all
to leader learning homework one of
india's best online classes
now today in this video we have a
question that is based on the topic of
parallelogram
the question says pqrs is a
parallelogram
l and m are points on pq and
sr respectively such that pl whereas pl
pl is equal to mr show that
l m and q s bisect each other
plm that means this part
lm is this and qs qss is basically
the perpendiculars and the diagonal one
diagonal bisect each other so
sr and pq are opposite sides of a
parallelogram that means this sr
and pq so they are equal because
opposite sides of a parallelogram are
equal
also pll is equal to rm pl is equal to
rm that is given
so if you subtract pq minus
pl and sr minus rm what you will get you
will get lq is equal to sm
whereas lq this is lq and that will be
equal to what that will be equal to sm
this part so now consider triangle smp
smp and triangle qlp qlp
alternate interior angles which one msp
this angle
and pql this angle alternate interior
angle similarly
smp smp and plq
and plq alternate interior angles
and sm is equal to lq that we have
already proved from third this part
so based on that triangle smp is
congruent to triangle qlp
this triangles now by asa criteria they
are congruent
now based on that sp is equal to pq
and mp is equal to
pl how corresponding parts of
congruent triangles so i hope you have
understood the concept very clearly
but still if you have any doubt do
comment in the comment box
and please like and subscribe our
channel for lido thank you"

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