Sum of All Angles in Quadrilateral is 360° (Theorem and Proof) Video Lecture

hello those for welcome welcome to this
presentation from rising pearl hum apke
hosaka destroy our Kamala Buddha so we
are talking about brand new CD series 8
jaha we are discussing quadrilaterals as
does the webisode number 3 plus the
Hammadi first maybe something we talked
about what is a quadrilateral and hamari
second webisode MCUs we talked about
different types of quadrilateral so so
as we are going to talk about the first
theorem involving a quadrilateral that
is sum of all angles is 360 degrees so
this is a pileup attacker to have what
is this theorem and then we are going to
find out guess I can give you can go
ahead and prove this so those are what
the theorem is telling us is that sum of
all angles from Alamitos quadrilateral
may we have actually four angles right
so the theorem is telling us that sum of
all angles of a quadrilateral is equal
to 360 degrees so how can we prove this
say Concord endoscopic as a
quadrilateral hamburger banality here or
at man djay let us call this
quadrilateral ABCD ABCD so what
basically goes though we are trying to
prove is after milimiters the
quadrilateral has four sides and four
angles so angle A plus angle B plus
angle C plus angle D yeoja marriage
Charro angle here is the angle A plus
angle B plus angle C plus angle D in
Charro angle ki sum total is 360 degrees
this is what the theorem is telling us
so I am kacica how we can prove this
those though such any account after let
us get started or not proof so I am
Tecate those Co we we saw if we start
with given what is given to us right so
we have a quadrilateral ABCD as shown in
the figure so you come contractually let
us give it a name let me say caterham a
B
see D yeah those the hamari
quadrilateral ABCD now those though
abdic okay so what is the next step next
step is what do we need to prove so we
need to prove that all internal angles
the sum sum of all internal angles of
the quadrilateral is 360 degrees that is
angle a angle B angle C and angle D
Charro angles key sum total should be
360 degrees this is what we have to
prove right so now though so we are
going to start the proof and we join one
diagonal of the quadrilateral so how
many have it was the point a and C Co we
have joined like this by drawing a
straight line between point A and C and
this is the diagonal of a quadrilateral
yeah a diagonal of the quadrilateral
similarly those a BD would have been
another diagonal so also um the AC joint
here AB AC cabbage' you could have
joined BC also so idea is just that we
join one diagonals of the quadrilateral
in this case having a AC Co joined key
here so now next what happens so now
those go up they cook it now in triangle
ACB so up up capacity though triangles
one day he right you have a triangle a
CB Yap cake triangle here and you have a
triangle a C D this is your second
triangle so this hump a break occurs
ahead he up taking a in triangle ACB a
Seabee is triangle me I am I'm alone my
angle CA B that is angle C a B Evalia
angle plus angle ABC a b c that is this
angle and angle a CBA Stevie Evalia
angle so so in Tina angle key sum total
is 180 degrees is 180 degrees Q because
we know that sum of all angles in a
triangle
is 180 degrees right because angle
triangle a B C it's a triangle or mm all
over there's a triangle may jaha marry
teen angles in key sum total is 180
degrees yellows the Homme neige we have
seen this this is a theorem so similarly
those of a Chile let us let us continue
to move forward so a B similarly those
Bob they ho gaya happy we actually now
similarly can see that in triangle a CD
zombies second triangle here is triangle
by those of this angle Plus this angle
Plus this angle is again 180 degrees
right because in triangle a C D all
these three angles sum total of three
angles is again 180 degrees so saviem
the Quebec Canada Hockey America yet
triangle 3a CB muhabba these three angle
kisum was 180 degree and then we have
these three angle P some also 180 degree
so other paheli Valley condition Tomcat
ahead condition 1 or is focus a
condition 2 then we can add condition 1
and add condition to right so I got a
macro things also then what happens so
adding 1 & 2 we get Joe changgil have 1
2 3 4 5 6
they are equal to 180 degree plus 180
degrees right yeah Nikki we can say that
we can say that those two now so I got
up Charo the rupture angle co-ed
birthday hook so now this angle Plus
this angle becomes angle a right so
similarly at this angle Plus this angle
becomes angle C so similarly the storm
the day hockey so angle A plus angle B
plus angle C plus angle T char angle put
together will be 360 degrees and those
this is what we wanted to prove Homme
neige should wat ETA Cody quadrilateral
key and we wanted to prove that some
total of all four angles of a
quadrilateral is equal to 360 degrees so
the serve we finally have we have proved
what we started out are trying to prove
so this is how we can tell that sum of
all internal angle of a quadrilateral
will be always equal to 360 degrees so
so ugly where we survey we are going to
meet with another proof so typically
shukriya taniwha