L8 : Parallelogram Numerical - Quadrilaterals, Maths, Class 9 Video Lecture - Class 9 | Best Video for Class 9

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two parallel lines LLM and are
intersected by a transversal P we have
to prove that the quadrilateral form by
these bisector of these interior angles
as a time they say that this angle is
close this angle so let me give a number
1 & 2 so if these angle is equal to this
angle let me number this is 3 and this
is 4 so it is given that angle 1 is
equal to angle to angle 3 is equal to
angle 4 so to prove this this is a
rectangle let this be angle 5 so I have
to prove one angle is my degree I have
to prove this angle 5 is 90 degree and I
have to prove that it is a parallelogram
it's a beast value to CD and weak use
valid to anything so let's first prove
that the angle is 90 degree
see angle 1 plus angle 2 plus I get 3
plus angle 4 is how much 180 right angle
1 plus angle 2 plus angle 3 plus angle 4
is 1 1 because angle 1 plus 2 is what
this angle s AC 3 plus 4 is what AC are
and these two are corresponding angles
angles corresponding angles sorry these
are angles are the same side interior
angle on the same side interior angles
on same side of
transversal it is angle line Ln line M
are parallel so interior angles on the
same side anger when pressing will do an
angle 3 plus angle code these angles is
180
okay so now angle 1 is what equal to
angle 2 so I can say this is angle 2
plus angle 2 similarly angle 4 is what
angle 3 is equal to so with this I get 2
plus angle 3 is what 90 degree okay now
in triangle a C D a CD angle 2 plus
angle 3 plus angle 5 is 1 180 degree
angle some property of triangle so I'm
going to plus 3 is 90 we already have
plus angle 5 is 1 what ideally so with
this angle 5 is 90 degree first part is
true right angle 5 is 90 degree that is
fruits let me write it here might leave
okay similarly similarly what we can do
is we can actually prove that angle this
is also a TV we can write this number
side 1 you can see this this is 6 7 8 9
10 same thing we can do and we can prove
that this angle is also 90 dB okay Oh a
better way is if you see let's make this
as 6 okay so 3 plus 4 is equal to 6 plus
7 because they are all triangle finger 3
plus 4 is equal to angle 6 plus
single-sim okay and in this it is also
given angle 6 is equal to angle 7 now
given so 3 plus 4 is equal to 6 plus 7
so what is 3 4 6 7 so what is 4 4 is
equal to angle 3 so you see the angle
for I can see angle 3 similarly 7 angle
six swaggin self-similar bangle six so
but this you can say that I get three is
equal to magnetic if angle three is
equal to angle six if you see they are
all triangle if a B is parallel to CD
so with this a we span it to see correct
baby Spaniard CD three is equal to six
okay similarly we can prove that ad is
parallel to BC correct now I became
prove that it is a parallelogram and if
I prove that one angle nine degree that
means it is a rectangle okay so it is a
rectangle why because it is a
parallelogram and one angle is 90 degree
so we have to prove that the bisectors
of the angles of the parallelogram forms
a rectangle that means this I be able to
prove that this angle is 90 degree unit
is a parallelogram or if we can prove
that all the angles are 90 degree again
show that it is a rectangle okay so let
me put some numbers to this this is
angle 1 2 3 4 5 6 7 & 8 so it is told
that this ASDs CQ dpr bisectors of this
angles so it is given that angle 1 is
equal to angle to angle 3 is equal to
angle 4 and L 5 is equal to minus 6
angle 7 is equal to angle it so we have
to do that this is 90 degree to prove
okay so to prove this what we can do is
if you add angle 1 plus 2 Plus 3 plus 4
what is this this will be 180 degree
right interior hang on the same side of
the transmission now angle 1 is equal to
what angle to sell see
chuckling will do now angle for is equal
to what angle three and why I've done
this vide into place I buy a place for
be three by not three before because I
have to prove that angle 2 plus C's 19
and that's why I'm writing this equation
in the form of angle to entry so with
this I get angle 2 plus angle 3 is 90
degree if I angle to entry is 90 degree
this angle is over what so let me call
this as angle line so angle line will
also be 9 degree why because angle 2
Plus 3 plus angle 9 is what 180 degree
some of the angle of a triangle triangle
D si this is 90 so this has to be 90 so
angle line is 90 degree angle line is I
need any angle PSR will be equal to
angle line particular opposite angle and
therefore angle PS R is 90 degree that
is one equation similarly I can put
through that PQ R is also 90 degree
similarly you start on this side angle
set 6 plus 5 plus 6 plus 7 plus 8 is 180
that means 6 plus 7 is 90 right 6 plus 7
is 90 this angle is 90 angle 10 let's
suppose so this angle is also 90
okay now we have to prove angle PNR of
90 degrees okay that is pretty easy to
prove
now if you see angle 4 plus 5 we can
easily prove s 90 why see angle 3 plus
angle 4 plus angle 5 plus angle 6 he'll
also be 180 degree because a DS parallel
to BC interior angle now we have to
prove that 4 plus 5 is 9 degree so I can
just write this equation in angle 4 and
5 thumbs angle 3 is equal to angle 4
similarly 6 is equal to angle 5 all
right it comes up angle 5 this is 180
degree so you saw this you get angle 4
plus angle 5 is equal to my if angle 4
plus 5 is 90 degree so let's suppose
this is 11 so angle 11 will also be 90
degree because angle 11 plus 4 plus 5 is
9 degree why did he be 4 plus 5 is
already 90 degree you just mentioned 11
plus 1 plus 5 is one angle properly this
is 90 this has to be 90 so this angle 11
is the integral so angle 11 is nothing
but angle spq that you wanted to prove
so we have similarly we can prove this
angle of 90 degree because this angle
Plus this angle angle 1 plus angle 8
will be 90 degree so we can do this
angle sorry angle 1 plus angle 8 will be
90 degree so angle art will also be 90
degree so thus we can prove that in in
this quadrilateral PQRS all the angles
are 90 degree and thus it is a rectangle
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