Class 10 Exam > Class 10 Videos > Example Pythagoras Theorem- 1
Example Pythagoras Theorem- 1 Video Lecture - Class 10
FAQs on Example Pythagoras Theorem- 1 Video Lecture - Class 10
| 1. What is Pythagoras Theorem? |  |
Ans. Pythagoras Theorem is a fundamental concept in geometry that relates to right-angled triangles. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In mathematical terms, it can be represented as a² + b² = c², where 'a' and 'b' are the lengths of the two sides and 'c' is the length of the hypotenuse.
| 2. How can Pythagoras Theorem be applied in real-life situations? | |
Ans. Pythagoras Theorem has numerous real-life applications. One common example is using it to find distances. For instance, if you know the lengths of two sides of a right-angled triangle, you can use the theorem to find the length of the third side, which represents the distance between two points. This concept is extensively used in navigation, engineering, construction, and even in everyday activities like measuring distances.
| 3. Can Pythagoras Theorem be used for triangles that are not right-angled? | |
Ans. No, Pythagoras Theorem is specifically applicable to right-angled triangles only. It does not hold true for triangles that do not have a right angle. In such cases, other trigonometric ratios like sine, cosine, and tangent are used to determine the relationships between the sides and angles of the triangle.
| 4. Who discovered Pythagoras Theorem? | |
Ans. Pythagoras Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. Pythagoras was a philosopher and mathematician who lived in the 6th century BC. Although the theorem had been known to the Babylonians and ancient Egyptians, Pythagoras is often considered the one who proved the theorem and provided a mathematical proof for it.
| 5. Can Pythagoras Theorem be generalized to higher dimensions? | |
Ans. Yes, Pythagoras Theorem can be extended to higher dimensions. In three-dimensional space, it can be generalized as a² + b² + c² = d², where 'a', 'b', 'c', and 'd' represent the sides of a rectangular prism or a cuboid. Similarly, in n-dimensional space, the theorem can be generalized as the sum of squares of all the sides being equal to the square of the longest side. However, visualizing and proving the theorem in higher dimensions becomes more complex.
Text Transcript from Video
/ friends this video on triangles part
41 is brought to you by exam feel calm
no more fear from exam before watching
this video please make sure that you
have washed part 1 - part 40 from a
bushel you have to prove that three
times sum of squares of sides of a
triangle is / - four times sum of
squares of media of the time
let's take is triangle ABC so we have to
draw a median also hence let's draw the
median D is the midpoint he is a big
point F is the midpoint it is all the
median a de and now my construction is
done so we will group that three times
on the squares the sides of the triangle
that is three times more squares is a
triangle is nothing but all sector
triangle a B square plus BC square plus
KC square this is equal to 4 times
pirate minion that is a d square plus B
square plus FC square we have to prove
this clue this will use the deviation
which we have derived last example this
is the complex machine that's why I'm
doing this out of the last issue so in
the last we should we have to prove that
a B square plus DZ square was equal to
twice of a d square plus BD square that
is something we should have done last
example right and this is nothing but
twice of ay T Square and she got we d
square right DC because I am looking for
a DB C is all sides and medians only so
write VC by this comes out to be twice
of ay square plus VC square by four so
what I need to do more this is nothing
but a d square plus VC square point that
is what we can see we are not to remove
by 2 here what I can do is this is
nothing but for a d square plus B
and this is nothing but here we square
plus a cz correct or I can take in the
center so I will get this equation to a
B square plus BC square is equal to 480
square plus BC square this is my
equation 1 similarly if you take these
two sides instead of a B and a C if I
take a B&B see this time so what I'll
give you a piece where you should only
see I'm taking we see super this time I
will get but oh you should have ad
because he was here
I'll get me here we square plus the
other side this is e square and in the
other case what I will get if I take AC
and PC and it who is v square plus BC
square this will be equal to 4 CF Squire
the medium square plus the next thing is
EB square I take a C f/c cm square and
got excited
so get three equations have one equation
one with a ladder so get you into may be
square plus BC square plus DZ square
plus kV square plus BC square plus BC
square by at all all these three this
one
tippin's history we are three Krishna
grade who we do twice a B squared y CC
square plus BC square and this is
nothing but 480 square plus B square
plus four CX plus AV square plus DZ
square plus BC square so what I get and
let's just solve this I get four into AV
square plus
DZ square plus DZ square minus AV square
plus BC square or EC square plus BC
square this is equal to 4 into a
t-square plus B's plus CL fish well all
right let's all then this becomes 3 into
EP square plus DZ square is equal to 4
into d square plus B's plus C X and that
is what I'm supposed to be correct I
prove it I will use the derivation
derived from the last slide
let's move that 3 times side square is /
- 4 times DS here angle ACB is 90 CDs
palette we need to prove that Behe
square of a chi-square is going to be
divided
so what approach will follow will first
try to find me she spied EC square and
then you see the value C you find BC
square will take we have done such quick
question let's try the bond ADC triangle
to be sneaky and trying to fix the code
bring it back we want to fight BC square
and take triangle this triangle I get
two good triangle ABC you try to prove
they're similar and then by the
corresponding side pressure will find BC
square so going to find BD AC square you
take this triangle triangle triangle ABC
pull the data similar and then find
HD square so let's see this becomes
reaching - feel my this is 19 19 - a is
180 so this is 90 minus a this is a why
because C is also 90 degree this is a
this becomes 19 - all right fine VC
square 5 BC square B code will compare
triangle
and like them babies all right
that is will compare triangle a B C and
triangle the STIs right trying them
correct what C is 90 C is 19
I can easy take it easy
so we'll say that in triangle is a we C
is equal to angle D by construction
angle B is equal to angle C that is 90
degree so triangle is ABC since they are
similar we can take the side so we have
e vc square so we need this side sorry
really first people for AC square plus C
square this side and this thing so I'm
going to take this side by this
hydration this is so what we get AC by
ad is equal to AP by H see what I get is
e square is equal to gave me in this ad
Amy this is my first equation simply you
take to get VC square I'll take time
back to so I'll take in triangle - and
I'm the ABC I'll prove their single so
let me take triangle to drag on ABC
so triangle 2 is nothing but C D B D is
right crankin so in triangle ABC C is
right triangle you think in this and
this B is B is Palma - this is my
structure
C is equal to T 90 degree I will be
happy for my construction right so we
can see that in triangle C
we see I'm get B is equal to angle D 90
degree right angle B is equal to angle B
my construction right so we can see that
I can see the similar to triangle ABC
since they are similar
I can our mind BC ratio so I take this
side
in this edition so I think VC by VD in
my busy but I get VC square is equal to
a me correct this individually I divide
1 by 2 sorry 2 by 1 I will get VC square
by a cheespider
it's nothing but a me by a a BB cancer
this is nothing but we need Levi and
that is what we wanted to prove correct
you observe that we need BC square and
DZ square you get VC square we prove
that angle to my angle ABC is a triangle
into one triangle ABC is similar you get
AC square you can I come on an angle
triangle ABC similar it does we got me
she squatted AC square we divided this
take it down let's take one more example
if it is perpendicular to BC in this
example we have to prove that AV square
plus V V squared over 2 BD square plus
BC square
so very simple question actually AV
square plus VB square this sign Swedish
product to study
DD square AC squared V DS / on this
right and this thing if you take these
sides you see what again this triangle
and this triangle triangle 1 and
triangle and you see ad square inside of
the moment in go to find them so let me
write the equation first cross triangle
1 cv d square L will be AV square plus
Davy's were correct in trying that one
similarly in trying to do all so I'll
write T square is nothing but for any
squares EB square minus B Square you see
they're also ad square will be VC square
ends the hypotenuse minus CV square all
right and both are same VD square this
is 1 this is 2 so I can equate these two
equation or get a B Square minus BD
square is equal to AC square minus CD
square I take this this side to this
side
so what I'll get AV square plus B square
is equal to be nice where Plus is in
square and that is what I was supposed
to
Lukie where is it is observed that we
got this type this type is like this
then we found that the set is common so
we use Pythagoras theorem liquid assets
very simple vision thank you visit exam
viacom to watch free education videos
try free on my debts get the best
quality study materials study from the
best tutors and mentors and much more
thanks again
41 is brought to you by exam feel calm
no more fear from exam before watching
this video please make sure that you
have washed part 1 - part 40 from a
bushel you have to prove that three
times sum of squares of sides of a
triangle is / - four times sum of
squares of media of the time
let's take is triangle ABC so we have to
draw a median also hence let's draw the
median D is the midpoint he is a big
point F is the midpoint it is all the
median a de and now my construction is
done so we will group that three times
on the squares the sides of the triangle
that is three times more squares is a
triangle is nothing but all sector
triangle a B square plus BC square plus
KC square this is equal to 4 times
pirate minion that is a d square plus B
square plus FC square we have to prove
this clue this will use the deviation
which we have derived last example this
is the complex machine that's why I'm
doing this out of the last issue so in
the last we should we have to prove that
a B square plus DZ square was equal to
twice of a d square plus BD square that
is something we should have done last
example right and this is nothing but
twice of ay T Square and she got we d
square right DC because I am looking for
a DB C is all sides and medians only so
write VC by this comes out to be twice
of ay square plus VC square by four so
what I need to do more this is nothing
but a d square plus VC square point that
is what we can see we are not to remove
by 2 here what I can do is this is
nothing but for a d square plus B
and this is nothing but here we square
plus a cz correct or I can take in the
center so I will get this equation to a
B square plus BC square is equal to 480
square plus BC square this is my
equation 1 similarly if you take these
two sides instead of a B and a C if I
take a B&B see this time so what I'll
give you a piece where you should only
see I'm taking we see super this time I
will get but oh you should have ad
because he was here
I'll get me here we square plus the
other side this is e square and in the
other case what I will get if I take AC
and PC and it who is v square plus BC
square this will be equal to 4 CF Squire
the medium square plus the next thing is
EB square I take a C f/c cm square and
got excited
so get three equations have one equation
one with a ladder so get you into may be
square plus BC square plus DZ square
plus kV square plus BC square plus BC
square by at all all these three this
one
tippin's history we are three Krishna
grade who we do twice a B squared y CC
square plus BC square and this is
nothing but 480 square plus B square
plus four CX plus AV square plus DZ
square plus BC square so what I get and
let's just solve this I get four into AV
square plus
DZ square plus DZ square minus AV square
plus BC square or EC square plus BC
square this is equal to 4 into a
t-square plus B's plus CL fish well all
right let's all then this becomes 3 into
EP square plus DZ square is equal to 4
into d square plus B's plus C X and that
is what I'm supposed to be correct I
prove it I will use the derivation
derived from the last slide
let's move that 3 times side square is /
- 4 times DS here angle ACB is 90 CDs
palette we need to prove that Behe
square of a chi-square is going to be
divided
so what approach will follow will first
try to find me she spied EC square and
then you see the value C you find BC
square will take we have done such quick
question let's try the bond ADC triangle
to be sneaky and trying to fix the code
bring it back we want to fight BC square
and take triangle this triangle I get
two good triangle ABC you try to prove
they're similar and then by the
corresponding side pressure will find BC
square so going to find BD AC square you
take this triangle triangle triangle ABC
pull the data similar and then find
HD square so let's see this becomes
reaching - feel my this is 19 19 - a is
180 so this is 90 minus a this is a why
because C is also 90 degree this is a
this becomes 19 - all right fine VC
square 5 BC square B code will compare
triangle
and like them babies all right
that is will compare triangle a B C and
triangle the STIs right trying them
correct what C is 90 C is 19
I can easy take it easy
so we'll say that in triangle is a we C
is equal to angle D by construction
angle B is equal to angle C that is 90
degree so triangle is ABC since they are
similar we can take the side so we have
e vc square so we need this side sorry
really first people for AC square plus C
square this side and this thing so I'm
going to take this side by this
hydration this is so what we get AC by
ad is equal to AP by H see what I get is
e square is equal to gave me in this ad
Amy this is my first equation simply you
take to get VC square I'll take time
back to so I'll take in triangle - and
I'm the ABC I'll prove their single so
let me take triangle to drag on ABC
so triangle 2 is nothing but C D B D is
right crankin so in triangle ABC C is
right triangle you think in this and
this B is B is Palma - this is my
structure
C is equal to T 90 degree I will be
happy for my construction right so we
can see that in triangle C
we see I'm get B is equal to angle D 90
degree right angle B is equal to angle B
my construction right so we can see that
I can see the similar to triangle ABC
since they are similar
I can our mind BC ratio so I take this
side
in this edition so I think VC by VD in
my busy but I get VC square is equal to
a me correct this individually I divide
1 by 2 sorry 2 by 1 I will get VC square
by a cheespider
it's nothing but a me by a a BB cancer
this is nothing but we need Levi and
that is what we wanted to prove correct
you observe that we need BC square and
DZ square you get VC square we prove
that angle to my angle ABC is a triangle
into one triangle ABC is similar you get
AC square you can I come on an angle
triangle ABC similar it does we got me
she squatted AC square we divided this
take it down let's take one more example
if it is perpendicular to BC in this
example we have to prove that AV square
plus V V squared over 2 BD square plus
BC square
so very simple question actually AV
square plus VB square this sign Swedish
product to study
DD square AC squared V DS / on this
right and this thing if you take these
sides you see what again this triangle
and this triangle triangle 1 and
triangle and you see ad square inside of
the moment in go to find them so let me
write the equation first cross triangle
1 cv d square L will be AV square plus
Davy's were correct in trying that one
similarly in trying to do all so I'll
write T square is nothing but for any
squares EB square minus B Square you see
they're also ad square will be VC square
ends the hypotenuse minus CV square all
right and both are same VD square this
is 1 this is 2 so I can equate these two
equation or get a B Square minus BD
square is equal to AC square minus CD
square I take this this side to this
side
so what I'll get AV square plus B square
is equal to be nice where Plus is in
square and that is what I was supposed
to
Lukie where is it is observed that we
got this type this type is like this
then we found that the set is common so
we use Pythagoras theorem liquid assets
very simple vision thank you visit exam
viacom to watch free education videos
try free on my debts get the best
quality study materials study from the
best tutors and mentors and much more
thanks again
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Nov 23, 2024 Last updated |
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