Some important points regarding Areas of Triangles Video Lecture - Class 7

hello friends this video on perimeter
and area part 8 is brought to you by
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one more interesting thing is that that
even inside triangles we can find more
travel so there are smaller tangles
inside a bigger triangle that's
interesting right so let us have a look
at this one so in this diagram what do
you see so overall what is this this is
nothing but a triangle let's name it
let's call this as a b c so what is a b
c so ABC is a triangle now let us call
this point as d now what is a BD this is
also a triangle what is ABC that does
also attract that so basically here we
see that triangle abd that is the green
one and the triangle ABC that is the
orange one these two triangles are
present inside the triangle ABC so this
is a scenario where we find triangles
inside triangles now in this case again
so looking at this and I know do you
think that triangle abd that is triangle
abd the green one and triangle ABC are
these two congruent what do you think
about them because now why is it
important to know if these two triangles
inside the bigger triangle are congruent
or not because if these two triangles
are congruent that would actually mean
that area of this triangle would be
equal to the area of this triangle so
let us find out if they are congruent or
not so when you compare these two
triangles you see that this is a right
angle this is also a right angle right
similarly this ad is a common sight for
both the triangles now in case we are
given that this triangle ABC if this is
an isosceles triangle or an equilateral
triangle then we also have these sides
equal that is a B and a C are equal so
with these kind of criteria if we find
that triangle abd is congruent to try
ABC if they are congruent that would
mean that area of triangle abd is equal
to the area of triangle a D C and what
would that mean that would actually mean
that area of triangle abd is equal to
area of triangle ABC and this is equal
to half into area of triangle ABC so
basically if the areas of these two
smaller triangles are equal that would
mean that area of each small rectangle
triangle is half the area of the bigger
triangle but all of this was possible
only because these two triangles were
content now let us look at another
scenario so here also we have one
triangle let's call this triangle also
as ABC so ABC is a bigger travel and
inside ABC you have a triangle abd you
are not the triangle ADC so here also
you see that there is one big triangle
inside the big triangle you have two
smaller triangles but in this case do
you think that the area of triangle abd
will be half the area of triangle ABC
now whenever you look at the second
scenario now in the second scenario we
see that the area of triangle abd is not
equal to the area of triangle and we see
so why do we say this in case of this
scenario because here also these are a b
b and a DS they are two small triangles
inside a bigger triangle that's because
in this case this triangle the blue
triangle and the pink triangle they are
not congruent to each other so that
means that only if two triangles are
congruent they overlap completely with
each other
and therefore they cover equal areas so
if two triangles are congruent then they
will always have their areas equal so
whenever you have any scenario of the
sort where you are have seeing smaller
triangle
inside fabula gram or smaller triangles
inside a rectangle or another triangle
first of all you need to evaluate if
those smaller triangles are congruent to
each other only then you can conclude
that their areas are same so if two
triangles are congruent they have equal
areas but if they are not congruent they
do not have equal areas however many
times you might think that okay now if
we have two triangles which have equal
areas so will they be congruent so we
are just telling the vice-versa like we
saw in the previous slide that if two
triangles are congruent they have equal
areas now in in on the screen we see two
triangles with equal areas so let's say
that this is triangle ABC and this is
triangle d e f so now in this case let's
say that area of triangle ABC is equal
to area of triangle d EF so this is
given we know this as a matter of fact
now if I ask you that these two
triangles are congruent or not so do you
think they have congruent well in this
case they are definitely not congruent
now forget about the criteria for
congruence if you try to overlap these
two triangles over each other they will
not cover each other completely so
therefore even though this fact is true
that if two triangles are congruent they
have equal areas but the vice-versa is
not true that means two triangles with
equal areas are not necessarily
congruent they might be congruent but
they might not be congruent so if two
triangles have equal areas they may or
may not be congruent so this is a very
important concept thank you please visit
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