Examples: Properties of Parallelogram(Part 1) Video Lecture | Advance Learner Course: Mathematics (Maths) Class 7

hello friends this video on
quadrilaterals part 15 is brought to you
by exam for calm no more fear from exam
so now is the time to solve some
questions based on these properties of
parallelogram question number one find
XY and Z so here we have a pad milligram
so you see only one angle is given and
all others we need to find out so do you
think we'll be able to find it out yes
of course because we know certain
properties of parallelogram the first
property that we know is opposite angles
are equal now since opposite angles are
equal therefore very easily we found out
one angle Y will be equal to 100 degrees
so one angle we already found out the
second property that we know is adjacent
angles are supplementary that is sum of
the adjacent angles is equal to 180
degrees so therefore we can say that X
plus 100 degrees is equal to 180 degrees
because X and 100 degree they are
adjacent angles therefore X will be
equal to 180 minus 100 which is 80
degrees so this is how we found out the
value of X now what about Z again Z and
X are opposite angles therefore Z will
also be equal to X which is equal to 80
degrees therefore the value of x Y Z
would be eighty hundred and eighty
respectively question number two find
XYZ here again we have a parallelogram
where we have to find out these values
now let us look at this triangle now
even before we look at this triangle let
us first try to see which one can be
found can we find in the easiest
possible way the value of x can be found
very easily because if you look at X
what do you see now in case of a
parallelogram we know that the diagonals
they bisect each other so the diagonals
they like cross or
each other such that this part is equal
to this part so in this case first of
all let us try to name the figure so let
us call it a b c d so that would help us
in our calculations now here we see this
angle is equal to 30 degree and let us
call this angle as angle one so angle 1
will be equal to 3 degrees this is 3
degrees basically so this is 3 degree so
this will also be 3 degree why since BC
is parallel to ad opposite sides are
parallels in a parallelogram so these
are alternate angles now you look at
triangle a OD if this point is o so in
triangle a OD what would happen sum of
the three angles should be equal to 180
degree that is angle Z plus angle one
Plus this angle is given as 90 degrees
plus 90 degree should be equal to 180
degree now we already found angle one as
three degrees so 3 plus 90 would be 93
degrees therefore Z will be equal to 180
minus 93 which is equal to 87 degrees so
this would be the value of Z now once we
have found the value of Z we can very
easily find find the value of y Y
because Y will be equal to Z since BC is
parallel to ad so again these are also
alternate angles so therefore Y will
also be equal to 87 degree so now we
know Y we know said so we have to
calculate the value of X now to find out
X let us go to triangle D OC so in
triangle B OC X plus 3 degree plus y is
equal to 180 degree so therefore X plus
3 degree plus y y is nothing but 87
degree is equal to 180
therefore X is equal to 180 minus 90
which is equal to 90 degrees therefore
the value of x is equal to 90 degrees so
this is how we could find out the value
of x y and z question number three find
X Y Z so here again we have this
parallelogram say let's call it a b c d
now in this case let us see what can be
find very easily now we know that in
case of a parallelogram opposite angles
are equal so therefore we can say that Y
will be equal to 112 degree because Y
and hundred whether they are opposite
angles so we could find one canyon that
is y now let us look at triangle a B C a
triangle abd when you look at this
triangle abd we know that sum of the
three angles should be equal to 180
degrees so X plus y plus 40 degrees
should be equal to 180 degrees so X plus
y is 112 plus 40 is equal to 180 degree
therefore X plus 152 degrees is equal to
180 degrees or X is equal to 180 minus
152 degrees which is equal to 28 degrees
therefore the value of x is 28 degrees
so what is left out z now if you look at
Z Z will be equal to X that is because a
B is parallel to CD
therefore alternate angles would be
equal so therefore we can say Z it will
also be equal to 28 degrees question
number 4 can a quadrilateral ABCD be a
parallelogram if angle D plus angle B
is equal to 180 degrees so in order to
answer this first let us draw a
quadrilateral so let us say this is a
quadrilateral named a/b c/d
now in the question it is given that
angle B plus angle D is equal to 180
degrees that means basically the sum of
the opposite angles is equal to 180
degree does that mean that it has to be
a parallelogram now quickly recall the
properties of parallelogram a
quadrilateral is a parallelogram only
when the opposite sides are parallel but
this relation doesn't tell anything
about the opposite side string value the
second property is the opposite angles
are equal but here it says that the sum
of the opposite angles is 180 degree
which means that it they could be equal
they could be both 90 90
this may not be equal also right so
there is no surety that the opposite
angles would be equal third the property
says that this the sum of the adjacent
angles should be equal to 180 degrees
again nothing of that sort has been told
this question so looking at only this
criteria all we can see is ABCD may be a
parallelogram or may not be so it is not
necessary that just because the sum of
the opposite angles is equal to 180
degree it will be a parallelogram but
yes had the sum of the adjacent angles
being equal to 180 degree it would have
actually satisfied one of the properties
of parallelogram so in that is there its
chances would have enhanced let's look
at the second criteria can of
quadrilaterals be a parallelogram
if a be equal to DC equal to 8
centimeter that is a B is equal to DC
and a B is equal to 4 centimeter this is
4 and BC is equal to 4 point 4 so in
this case it is basically saying that
one pair of opposite sides are
but the other pair is not equal so this
will definitely not be a parallelogram
so it cannot be a parallelogram because
in parallelogram all the opposite sides
are equal if angle is equal to 70 degree
and angle C is equal to 65 degree which
clearly says that the opposite sides are
unequal so if opposite sides are not
equal then again it can never be a
parallelogram thank you please visit
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