Pythagoras Theorem - Triangle and Its Properties, Mathematics, CBSE Class 7 Video Lecture

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now we are going to learn about
Pythagoras theorem so Pythagoras was a
very famous Greek philosopher and
mathematician and he gave a very
interesting property on right-angled
triangle and you will see it for
yourself that how this property held do
find solution to a lot of problems that
involved a right-angled triangle so what
this theorem stated was basically
something like this so he said that if
you have a right-angled triangle like
this
let's now even before we talk about this
theorem let us first understand the
various terminologies related to a
right-angled triangle so whenever you
have any right-angled triangle let's
call this as a b c so this ABC is a
right-angled triangle where you have one
right angle that is 90 degrees now the
sign it which is opposite to this right
angle that is this side AC this is
called the hypotenuse now the base this
one is the base and this one is called
the perpendicular so perpendicular
hypotenuse and base these are the three
sides of the right angle triangle okay
now according to this theorem it's
saying that let's say that you have a
right-angled triangle such that the
let's say the length of the hypotenuse
is C the length of the base is B and the
length of the perpendicular is a and if
we assume that on each of these sides on
perpendicular base as well as hypotenuse
on each of them if we assume that we
draw a square let's say we draw a square
on the perpendicular that means the
square each side of the square
would be equal to a right similarly
let's draw a square on the base so that
means each side of this square would be
B and in a similar way we draw a square
on this hypotenuse so here each side
would be C so as per this theorem that
the area of this square that is what
would be the area of the square the area
would be C square because area of a
square is side into side so area of this
would be C square and area of this
square would be B Square and area of
this square would be a square so
according to Pythagoras theorem C square
is equal to a square plus B Square that
is the area of the square which is drawn
on the hypotenuse is equal to the sum of
the areas of the squares which are drawn
on the perpendicular and the base sides
respectively so this was the Pythagoras
theorem now you might be wondering that
how come he how come he was able to find
out such a complicated relation because
we started with a right-angled triangle
and then we blow up we had drawn squares
on each side of the triangle and then we
have you know kind of derived to this
relation well this is not how it was
derived now this theorem can be proved
in a number of ways so here we will look
at a proof of the Pythagoras theorem by
rearrangement so we will see that how we
can rearrange triangles and we can prove
that C squared is equal to a square plus
B square that is hypotenuse square is
equal to square of the base plus square
of the perpendicular so as per
Pythagoras theorem in a right-angled
triangle square of the hypotenuse is
equal to sum of the squares on the legs
legs would mean the base and the
perpendicular now even before we start
proving Pythagoras theorem let us try to
understand why Pythagoras theorem why do
we need this theorem where will this
theorem help us now let us think of an
example
let's say that you know how far your
school is from your home so this is your
school and this is definitely your home
so you know the distance of your school
from your home perfect and you also know
how far is the part from your school so
you know the distance of the school from
your home you also know the distance of
the path from your school now let's say
that on a holiday when you are at home
you feel like going to the park but you
do not know the direct route of the park
from your home because you always went
to the park through your school so what
would you do
so this is something which you normally
followed you went to the school and from
school you went to the park now on a
Sunday when you feel like going to the
park do you think that you would like to
follow this route wearing you first go
to school and then you go to the park
not really right you might feel like
preferring a route where you can
directly grow go from your home to the
park so in that case you might even
follow this path so in that case now
when you look at these this entire route
thing you see that it is a light angled
triangle and in this right angle
triangle which is the hypotenuse this is
the hypotenuse let's call it H and these
are the other two legs let us call this
as base let us call this as P that is
perpendicular now with the help of this
relation hypotenuse square is equal to
sum of the squares of the other two legs
using these two relations we can very
easily find out this distance H so
that's how pythagoras theorem can help
us in real-life problems let's say that
you want to climb on ladder to reach out
to the top shelves in your house maybe
you want to find out the book from the
top shelf where you cannot reach
normally so you need a ladder now you
are in a doubt that how exactly should
your old should you orient the ladder so
that you can reach that specific height
where you
because they it might be possible that
the ladder is too long so you actually
need to end it in a way that you are
able to reach that particular height so
how would you decide that so let's say
this is your this is the wall or these
are the shelves and this is your ladder
so the orientation of the ladder would
be decided by the distance of the foot
of the ladder from the foot of the wall
so this distance now this distance is
nothing but your base the length of the
ladder is nothing but H and this height
that the desired height where you want
to reach that height is let's say P so
again using the relation H square is
equal to P square plus B square you can
actually decide where exactly you should
place the ladder so in this way the
Pythagoras theorem can actually help in
a lot of real-life problems and that is
the significance of Pythagoras theorem
in fact based on Pythagoras theorem or a
lot of other mathematical relations had
been proved later thank you please visit
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