Triangles as part of Rectangles and Squares Video Lecture - Class 7

hello friends this video on parameter
and area part 5 is brought to you by
example comm know about your prom exam
so let us look at an interesting thing
having ever observed that inside a
rectangle you can have triangles just
draw a diagonal like this and what do
you see the rectangle is now has been
now split into two triangles so this is
one triangle and this is the second
triangle so now you have two triangles
located inside the rectangle now let us
do something more interesting about
these triangles inside the rectangles
let us first of all name the rectangle
let's say this rectangle was a B C and D
so the moment it is divided into two
triangles what are the two triangles the
triangles are triangle a b c and
triangle a d c now let us try to compare
these two triangles like by looking at
them they look quite similar to each
other but are these triangles exactly
congruent now by now you all know what
is congruence right when two triangles
are so much exact to each other that
they can exactly overlap each other then
we say that the two triangles are
congruent and there are certain rules to
prove whether two triangles are
congruent or not so let us try to
compare these two triangles so here we
see if you look at these angles both of
these angles are a right angle so
basically angle ABC is equal to angle
ABC is equal to 90 degree so these two
angles are equal now when you look at AC
AC is a common sight for both the
triangles so AC is a common side okay
now when you look at ad and BC we see
that ad is also equal to BC that's
because in a rectangle opposite side
are equal so with this what do we see
that in both these triangles there is a
right angle the hypotenuse is equal and
one side is equal therefore we can say
that triangle ABC is congruent to
triangle ABC by which congruence or by
which rule of congruent by RHS that is
right hypotenuse side criteria so by RHS
criteria these two triangles are
congruent so what are we trying to prove
by saying that these two triangles are
congruent so what we are trying to say
is now in this case if I ask you to find
the area of one of these triangles so
what would be the area of one of these
triangles now since both these triangles
are congruent that means their areas are
equal because they both exactly overlap
each other right that means they both
enclose the same area so therefore we
can say area of triangle ABC is equal to
area of triangle ABC now since both of
them have equal area so area of each
triangle is equal to half of the area of
rectangle ABCD so we derived a
relationship between the area of the
rectangle and the area of the triangles
which are located inside the rectangles
now why we did this that's because many
of times it happens that you are not
given the area of the rectangle but you
are given the area of the triangle
so if you know this relationship you can
very easily find out the area of the
rectangle nice so in a very similar way
triangles exist inside square as well so
when you actually draw a diagonal inside
the square it again gets split into two
triangles and with the same analogy here
also we see that triangle ABC so if we
call this a B C E and D so with exactly
the same analogy we see that ABC
triangle is congruent to triangle ABC by
RHS congruence now since both these
triangles are congruent therefore we say
that area of triangle
BC is equal to area of triangle ABC
which in turn is equal to half of area
of square ABCD thank you please visit
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