Construction of Right Angled Triangle: Given Length of One Leg and its Hypotenuse Video Lecture | Mathematics for Grade 7

hello friends this video on practical
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let us now move on to the type 4 where
we will learn how do we construct a
right-angled triangle now this is even
simpler now in your right angle triangle
all we need is the length of the
hypotenuse and the length of any one
side of the triangle
why that's because when you look at a
right angle triangle somewhat like this
we know that one angle is always equal
to 90 degrees so you already know the
value of one angle so all we need to
know is this hypotenuse that is the side
just opposite to the right angle and
then any one side whether the either the
base or the perpendicular any one of
them so basically for a right angle
triangle knowing the hypotenuse and any
one side can make you draw the complete
triangle so in this case we have to draw
a triangle ABC which is right angled at
a that means the 90 degree is at Point a
with the given lengths of hypotenuse and
one side so in this case what we do
first of all we draw the given side
let's say a B of the triangle which is
not the hypotenuse now in this type of
construction you will be given the
lengths of two sides when is the
hypotenuse and the other one is one more
side so first of all you draw that other
side not the hypotenuse do not draw the
hypotenuse you draw the other side so
let's see this is the other side of the
triangle let's say this is it perfect
okay then what do we do next then the
next thing that we do is we draw the
right angle because the because we know
it will always be given in the problem
that which angle in the triangle is a
right angle because angle C can be night
angle and B can be right angle angle a
can be right angle but in the problem
itself it would be written that this
triangle is right angled at a that means
you need to draw a 90 degrees at Point a
so how do you draw a 90 degree gain the
same process take your compass consider
a as the center draw an arc then
consider this point as the centre draw
an arc
consider this point as the centre draw
an arc so basically this is 60 degree
this one has
see degree this one is 120 degree in
between 60 and 120 is 90 degrees so you
draw one out by considering this point
has the center you draw another Nalco by
considering this point at the center and
the point where these two arcs intersect
when you join that point to point 8 you
get a 90 degree so you have drawn and
then a which is 90 degree so now what
are you left with you are left with the
value of the hypotenuse so I put in use
would be the side which lies exactly
opposite to 90 degree that means the
side line here and the length of this
side would be given daily so what would
you do you take the compass place it on
the ruler adjust its opening in such a
way that the opening is equal to the
length of the hypotenuse so once you
have done that you place the compass in
this way you case the tip of the compass
on point P and then you place the other
end which is the pencils on this line
and you will be able to draw an arc here
so what is this length now this length
is nothing but length of the hypotenuse
because we have adjusted the opening of
the compass equal to the length of the
hypotenuse so once you have drawn this
arc you would see that this arc in meets
this line at a point so this point is
nothing but Point C or the third vertex
of the triangle now you join BC and you
get this right angled triangle so this
enclosed area shows you that I can cut
triangle so this is how we draw a right
angled triangle so in right angle
triangle the first step is always to
draw the other side not the hypotenuse
draw the other side then draw the right
right angle and then you draw the
hypotenuse so let us quickly look at
this question construct an isosceles
right angle triangle ABC where
measurement of angle ACB is equal to 90
degree and AC is equal to 6 centimeters
so let's quickly have a look at the
rough sketch so in this let let's first
draw a right angle triangle and then we
we name it so let's see this is a
angle triangle which is right angle at
this point now as per the question angle
ACB is 90 degree that means C has to be
this point but C is the middle point so
this has to be C and ACB is 90 degrees
let's say this is a this is C this is B
so angle ACB is 90 degree AC is given a
6 centimeter and what else is given and
it and nothing else is given but we
learned that for a tight angle triangle
we need to know one side and we also
need to know the hypotenuse but in this
case we do not know the hypotenuse so
how do we manage with it so how do we
get to know that how do we draw this
triangle now in this case the catch is
here it sees that it is an isosceles
right angle triangle that means this
side and this side basically the other
two sides other than the hypotenuse they
are equal
so basically BC is also equal to 6
centimeters now you know two sides and
the included angle basically the side
angle side criteria so that is known to
you so you can very well draw this
triangle as well so even though it
doesn't satisfy the right RHS criteria
but it does satisfy the SAS criteria so
let us now proceed with the construction
so first of all we will draw the base
let us say this is AC so this is how we
have drawn easy then you might be
thinking that the rough sketch and this
doesn't resemble so what we have done is
made just inverted it and we are
basically going to draw it somewhat like
this so then this is a this is C and
this is B so if you want you can draw it
like this as well that doesn't really
make much difference so once you draw a
C then you draw the right angle which is
nothing but the angle C so you draw this
90 degree like this so this is your
angle C which is 90 degree and this is
AC which is 6 centimeters so once you
have drawn this now what the value that
you know is BC is also equal to 6
centimeters so this is BC which is 6
centimeter so what you do you
the compass places on a ruler adjust its
opening such that the opening was equal
to six centimeters now you take the same
compass considered Point C as the center
and then you mark six centimeters here
that is one option but in this case
since this is also equal to six
centimeters so you really do not need to
take a ruler and then adjust the opening
of the compass all you can do is take
the compass place it here like measure
it like this this distance so once you
have measured this distance basically
you have adjusted the opening of the
compass keep that opening same and place
it here and then you draw an archer with
the compass with what does this mean
this means that you have made sure that
this length is equal to this length so
you made sure that AC is equal to BC so
this point where this arc intersects the
existing line is the point B now when
you join a B you get a right-angled
triangle so this is a right angled
isosceles triangle because this side is
equal to the length of the side so you
see this is another this was another
interesting example where you are
drawing the right-angled triangles but
this doesn't satisfy the RHS criteria
because here you do not know the length
of the hypotenuse but you still could
draw the right angle triangle only
because it satisfies the SAS criteria
that a side angle side criteria so
sometimes you need to understand the
question and then follow the approach
that's because you should not blindly go
with this third thought that okay I have
to draw a right angle triangle so I need
the hypotenuse if I put in yusin's not
there right then I cannot draw it so
it's not like that so you have four
different criteria SSS s a is e is a and
averages so if any of the four criteria
is getting satisfied you should be able
to draw that triangle so with this we
have reached towards the end of this
lesson so this lesson was more about
practical geometry where you actually
draw things you draw different triangles
you draw parallel
so what I would advise you to do is do
not merely watch this video you take a
compiled sheet of paper ruler pencil and
actually draw these triangles only then
your idea of drawing a triangle would be
clear so I hope this lesson would have
helped you see you all in the next
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