Examples: Congruence of Triangles Criteria Video Lecture | Mathematics for Year 8

hello friends this video on congruence
of triangles part 9 is brought to you by
exam for calm
no more fear from exam question number 5
in Figure AC is equal to BD so this is
AC and this is BD and ad is equal to BC
that as this length is equal to this
length which of the following statements
is meaningfully written travel ABC that
is this triangle this triangle is
strangle ABC this triangle is congruent
to triangle a B D that is this channel
so this is done and abd so this is more
meaningful or it is more meaningful to
write that triangle ABC is congruent to
angle D ad so you see both of these mean
the same travel both of these mean the
same triangle it is just that we need to
find out which point corresponds to
tangle a to point a because the only the
order is changed triangle abd also means
this channel
Randall ba D also means the same
triangle but when you talk about
congruence we talk about the
corresponding vertices right so here
when you look at at a diagram what do
you see that if you compare the two
triangles so let's say in triangle ABC
and triangle abd if you start comparing
what do you see you see that a B is a
common sign right so a B is one common
side so this is equal n is equal to a B
then you see AC is equal to BD then you
have AC is equal to B like so that
actually means that if you actually
rotate this triangle
as a BB and you try to place it over to
angle ABC such that it overlaps with
triangle ABC then what do you need to do
you will have to overlap it in such a
way that this point a should come over
point B like you you actually need to
you know kind of reverse it and then put
it here so point a should actually fall
on point B and point D should actually
fall on point C right so that is what we
have seen from here so AC is equal to BD
and we also see that ad is equal to BC
so from this we see that since all the
three sides are equal to their
corresponding sides so we can say that
travel ABC is congruent to triangle now
a will fall on which part now any
corresponds to point B that is what we
understand then you go and you rotate
this travel the giver side it pays it
over travel ABC then point a false one
point B and where does point D fall
while defaults on point C right so point
D will fall on point C and what happens
to point B because in this triangle also
you have a point to be right so you are
just reversing this racket like this so
basically this point this D is going
here this a is going here correct so
what is happening to this B because this
side is also there so this B is actually
coming here so B is actually the
corresponding point of point E so when
we see triangle a B C so how would we
write what is the corresponding point
corresponding vertex for a corresponding
vertex for a is B next is point B so
what is the corresponding point for P
for B is a and what is the corresponding
vertex for C 4 C it is B so this would
be planted
be ad so this is more meaningful now I
would not say that this is incorrect
this is not incorrect if even if we
write that angle ABC is congruent to
triangle abd it is not incorrect but
this one is more meaningful because by
looking at this itself you can see that
point a corresponds to point B point B
corresponds to point a and Point C
corresponds to point B and I hope you
understood how do we find the
corresponding point you just need to
visualize the two travels and you need
to find out that if you want that
triangle to overcome in in this case if
you want the triangle to overlap with
triangle ABC then which point will fall
over which point and that is how you
find out them correspondence question
number six is triangle PQR congruent to
triangle ABC so these are the two
triangles which are given so let us see
in triangles P Q R and triangle ABC what
do we see we see that the measure of
angle is P is equal to angle C so angle
B is equal to angle C which shows that
if you know kind of we want to overlap
the two triangles you actually need to
rotate this strangle the other side such
that Point C coincides on Point P so
basically point B and Point C are
corresponding points we also see that
length AC is equal to length RT because
both of these are 2.5 centimeters not
only that we also see that CB which is 3
centimeter is equal to PQ which again is
3 centimeter so basically what do we see
we see that two sides and the angle
which is sandwiched between the two
sides are equal to the corresponding two
sides at the sandwiched angle so
therefore we can say that triangle PQR
is on gluant dragger
tangle ABC or CBS I think see be able to
do more meaningful and why by which
criteria this is congruent this is
called joined by SAS criteria the two
sides and the included angle of one
triangle is equal to the corresponding
sides and angle of the other triangle
question number seven is strangled EEF
or grow end to triangle ABC again let's
have a look
so you grandeur des and triangle e we
find that a B is equal to EF so this is
something which is given because the
measure is three point five centimeter
for each of them not only that we see
that angle a is equal to angle F and we
also see that angle B is equal to angle
E so basically we see that two angles
and one side and that to the side is
included between the two angles they are
equal in the two triangles therefore we
can say that the two triangles are
congruent by which congruence by as8
right area and which would be the
corresponding points so you see and then
e is equal to angle B so basically point
B will correspond to point a point a
will correspond to point F and point C
would correspond to angle to point B
therefore we can say that angle D EF is
congruent to triangle C be a again this
is more meaningful to be written like
this so once you have established the
fact that the two triangles are
congruent try to find their
corresponding points so that you can
I found the confluence statement
involving in full way so here if again
it was simple since Apple II and and
agree that equal that means if you try
to overlap them so you will have to over
overlap B and E over each other so that
the lines overlap because the apples are
the same
similarly angle a is equal to F that
meant that at the point E and point F
are the corresponding points thank you
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