Representation of Congruence Video Lecture | Mathematics for Year 8

hello friends this video on congruence
of triangles part 4 is brought to you by
exam 4 calm no more fear from exam now
when we talk about congruence of
triangles we see that the moment you
talk about two triangles which are
congruent like in this case these are
the two triangles are taking the same
two triangles as where there in the last
slide just that I have named them so the
first triangle is named ABC the second
triangle is named DF yeah now what have
we observed we observed that in order to
overlap these two triangles if you place
this triangle as it is over this
triangle do you think that they will
cover each other exactly no in order to
cover each other exactly you need to
rotate this triangle so the moment you
rotate this triangle in the clockwise
direction what happens you bring it to
the same orientation at as that of this
triangle right and what is the same
orientation
maybe you rotate it in this fashion such
that the triangle is in this pattern
let's say if this is ABC you rotate when
you rotate it in an orientation like
this d e f so only then you see that the
two triangles they exactly cover each
other so what does that mean that means
that there are certain points that that
means there are vertices of the triangle
which are corresponding to each other
for example a and D are corresponding
vertices similarly B and E are
corresponding vertices C and F are
corresponding vertices so basically what
we are trying to see is they are not
equal there is no equality basically but
the the row in which the vertex a please
in triangle ABC is the role which vertex
D plays in triangle d e f so vertex a is
in correspondence with vertex D
similarly vertex B is in correspondence
with vertex P in the same way vertex C
is in correspondence with vertex F
so this is the concept of Correspondence
so whenever two triangles are congruent
so their corresponding parts will be
equal now it is not only the
corresponding parts is not only with
regards to the vertices it is also with
regards to the sides and the angles for
example what would be the corresponding
angle of angle a so the corresponding
angle would be angle D similarly the
corresponding angle for angle B would be
angle E the corresponding angle for
angle C would be angle M now the
challenge now when you look at these two
figures it is very easy to see that okay
corresponding angle of angle B would be
angle E but the challenge comes when
when you have your triangles in this
fashion so when you have it in this
fashion the corresponding angle for
angle a is actually this angle which is
angle D so you actually need to identify
that in which orientation of the
triangle the two triangles are
overlapping each other so only
considering that orientation you will be
able to find the corresponding parts of
the two triangles and how do we
represent the correspondence so
correspondence is represented using this
symbol so the symbol of a line basically
where you have arrows on both sides so
how do we represent let's say in this
particular example we see that angle a
corresponds to angle B similarly angle B
corresponds to angle E and the C
corresponds to angle F so this is about
the correspondence of angles similarly
the sides would also be corresponding to
each other so for example the side a B
will correspond to which side this side
a B will correspond to the side de
similarly side AC will correspond to
side B F similarly BC would correspond
to EF so these are the corresponding
sides of the two congruent angles and
what about the corresponding vertices
the corresponding vertices
would be a corresponds to D B
corresponds to e and C corresponds to F
so these are the corresponding vertices
so anytime two triangles are congruent
their corresponding parts would also be
equal like that means their
corresponding silence or their
corresponding angles so they should also
be it will in fact these corresponding
sides or angles only decide whether two
triangles will be congruent or not and
how do we represent congruence
congruence is represented using this
symbol where you have the equality sign
and on top of that equality sign you
have a curve like this so if I want to
say in this case that triangle ABC and
triangle D EF are congruent how do we
write this we write it like this
triangle ABC is congruent to triangle d
EF so these are these are basically two
new symbols that you have learned one
symbol is for correspondence and the
other symbol is for confluence thank you
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