02 - Similar Triangles - Class 10 - Maths Video Lecture

the shape that we can see on the screen
is called a triangle and we are quite
familiar with the reason also because if
we split the term triangle we will get
two terms tri which means three and
angle would be these corner areas that
we get as a result of two lines
intersecting so quite easily I can say a
triangle is a shape with three angles
and now we can even try this okay with
three angles we can only have three
sides now just in case if you would like
to try then you can try making another
side and join it with these existing
sides and what you'll get is a different
shape with a fourth angle all together
and that particular shape can be called
a square rectangle or any other
quadrilateral but not a triangle because
a triangle is a shape with three sides
and three angles so we can say number of
angles actually relate to number of
sides a shape can have all right let's
go ahead and name this triangle as
triangle ABC now what I want to do is
with you guys a small exercise in which
I'll present to you many triangles of
different shapes and different sizes and
what you guys have to do is you'll have
to identify as many triangles as
possible that you find similar to
triangle ABC ok so here we go alright
supposing you actually identify these
similar triangles so can I ask you if
you also found these particular
triangles to be more similar to triangle
ABC even when there are so many other
triangles now how do you think we would
pick only these triangles to be similar
out of so many other triangles well the
reason is quite nicely given by geometry
which is a part of mathematics it says
we can call any two shapes or figures
similar particularly in case of these
triangles on the screen if their
corresponding angles are same so let's
let's say their angles are 70 degree 80
degree and 30 degree because we know
that the total angle measure of the
three angles in a triangle is always 180
degrees so 70 plus 80 plus 30 will give
us 180
now we can call these triangles similar
only when they will have the exact same
set of angles that is 70 80 30
throughout also they can only differ in
their sizes as much as they can they can
be smaller they can be bigger provided
that they always maintain their angle
and when they maintain their angle they
are actually maintaining their aspect
ratio and what I mean by aspect ratio is
let's say we assign their sides some
lengths so if smaller triangle is 3 4 5
then medium triangle is 6 8 10 and
larger triangle is 12 16 and 20 now on
what basis did I assign them these
lengths if I say that smaller triangle
is 3 4 5 then this is the aspect ratio
of the smaller triangle because it is a
ratio within a triangle of its sides so
3 is 2 4 is 2 5 is the ratio that we
will maintain in all of these triangles
so 6 is 2 8 is 2 10 will again give us 3
is 2 4 is 2 5 if we divided by 2
similarly 12 is 2 16 is 2 20 will also
give us 3 is 2 4 is 2 5 if we further
divided by 4 so what we are doing is we
are not only maintaining the angle
measure but also we are maintaining the
overall aspect ratio of the triangle but
there is a way in which these sizes must
vary and only then they shall be called
similar so let's learn that concept -
how about naming the smaller triangle as
DF and the larger triangle as G H I so
let us just ignore the larger triangle
for a moment and quite clearly we can
see the smaller triangle d EF is
actually half in size of the medium
triangle ABC and I am saying that
because all of its sides are actually
half in length as compared to the sides
of the triangle ABC so if you take their
ratio of the sides that is that is the
ratio of side de of smaller triangle to
its corresponding side a be in medium
triangle so we will get 3 upon 6 which
is nothing but 1 upon 2 so BC of medium
triangle corresponds to EF of the
smaller triangle so if we take the ratio
for is 2 8 and
we will get 1 upon 2 similarly DF upon
AC will give us 5 upon 10 which is again
1 upon 2 so we can see whenever we are
taking the ratio of the sides of both of
these triangles we are getting the
answer 1 upon 2 so this particular
number 1 upon 2 will be called the scale
factor and please note that this scale
factor is actually something really
important when we are constructing
similar triangles in geometry so as part
of geometrical terminologies we can say
in this case we are performing a scale
down on triangle ABC by a scale factor
of 1 upon 2 to get a smaller triangle d
EF now if we shift our attention to the
larger triangle GHI quite clearly all of
its sides are double in length with
respect to the sides of triangle ABC so
what is happening over here is that
there is a scale factor of 2 that is
involved because all of its sides are
doubled in length so we can definitely
say we are performing a scale up on
triangle ABC by a scale factor of 2 upon
1 or 2 to get a larger triangle GHI but
wait there is another possibility that
there will be another triangle which
will not only have the exact same angle
measure as triangle ABC but all of its
sides will also be exactly same or in
other words I can say it will be the
exact photocopy of our given triangle
ABC and in such a case whenever two
shapes or two figures are exactly the
same
then in geometry we call them congruent
so we can say triangle ABC and triangle
PQR are Quan grew and to each other now
what can we comment about the scale
factor over here scale factor is
definitely going to be just 1 why
because all of its aspects are the same
so these are the main ideas that we have
to keep in mind when we are constructing
similar triangles so now let us move on
and see if you have been given a
triangle how can we construct another
similar triangle out of it with the help
of geometrical instruments like compass
and straightedge
please hit like if you have understood
the whole concept behind similar
triangles or you have any queries please
post it in the comment section below and
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