Class 10 Exam > Class 10 Videos > Examples Similarity of Triangle- 6
Examples Similarity of Triangle- 6 Video Lecture - Class 10
FAQs on Examples Similarity of Triangle- 6 Video Lecture - Class 10
| 1. What is the similarity of triangles? |  |
Ans. The similarity of triangles refers to the property where two triangles have the same shape but may differ in size. In similar triangles, the corresponding angles are equal, and the corresponding sides are in proportion.
| 2. How can we prove that two triangles are similar? | |
Ans. Two triangles can be proven to be similar by satisfying any one of the following conditions:
- Angle-Angle (AA) similarity: If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.
- Side-Angle-Side (SAS) similarity: If one pair of corresponding sides is in proportion and the included angles are equal, then the triangles are similar.
- Side-Side-Side (SSS) similarity: If all three pairs of corresponding sides are in proportion, then the triangles are similar.
| 3. How do we find the corresponding sides of similar triangles? | |
Ans. To find the corresponding sides of similar triangles, we can set up a proportion. By comparing the lengths of corresponding sides, we can write an equation and solve for the unknown lengths. For example, if the ratio of the lengths of two corresponding sides is 2:5, we can set up the proportion x/2 = y/5, where x and y represent the unknown lengths.
| 4. Can similar triangles have different areas? | |
Ans. Yes, similar triangles can have different areas. Although the shape and angle measurements are the same, the area of a triangle depends on the lengths of its sides. Since similar triangles can have different side lengths, their areas can also differ.
| 5. How can we apply the concept of similar triangles in real-life situations? | |
Ans. The concept of similar triangles finds applications in various real-life situations, such as:
- Architecture and construction: Architects and engineers use similar triangles to scale down or up the dimensions of buildings or structures.
- Map scaling: Cartographers use similar triangles to accurately represent large areas on a smaller map.
- Shadow problems: By using similar triangles, we can determine the height of an object or the length of a shadow based on the length of a known shadow and its corresponding object's height.
Text Transcript from Video
friends this video on triangles part 26
is brought to you by exam feel calm no
more fear from exam before watching this
video please make sure that you have
watched part 1 to power 25
take for example ABC and EMP our two
right triangles right angle and B at M
respectively you have to prove that
triangle ABC this triangle is similar to
triangle a M so first let us draw this a
b c which one is right triangle ABC like
this let's draw like a we see why
because you see you saw that B is the
right triangle side or like this so true
they were similar I'll draw a similar
triangle like this then also it will be
right triangle it should be empty why
because it is ABC and a MP mayrose if
you see any right right now to prove
they're similar first thing is these to
hang over scene done deal and if we can
prove that with an angular same audition
so on so if you see the angle ABC this
triangle right triangle a MP this
triangle right angle a is common so
angle a is equal to angle a now since we
have seen that what if I got a similar
let's write the steps step says in
triangle B AC and triangle M AP all
right angle BAC is equal to angle M AP y
same angle or you can write by
construction also an angle ABC is equal
to angle a empty y 90 degree therefore
these two angles are equal we can say
that triangle V is similar to triangle m
AP so let's take number problem the
question says E is a point on side C be
produced of an isosceles triangle ABC
with a B is equal to EC a B is equal to
BC this is a side CB produced this is
the point II a name is equal to AC ad is
parallel to BC and he gave his pattern
to AC you have to prove that triangle
abd is similar to EFC so we see abd this
is 90 so we draw a triangle like this
it's cut this this is one triangle this
is one triangle a B D D is 90 degree we
can see AV e sempre triangle abd is
similar to EF CBO to prove that this is
e this is f this is e CF son EC EC and
has two identity and if you see M is 90
not to prove both the triangles are
similar
first thing is angle D is equal to angle
F dot d with a 90 now we have to prove
either a is equal to e or B is equal to
C if you prove any of this are polymers
so on see first thing that comes to our
mind when I can we say a B is equal to
EC that is both hangers are similar so
this is left repose X so this becomes X
- that makes simple to angle X - helix
into English - why because a B is equal
to H now if you see in triangle be a D
angle B is X and angle C EF c EF angle C
is go to X dash and here is our solution
Phi because is X equal to X dash we can
see that angle B is good doing a see D
is equal to f is already put with 90 so
they are similar so now let us write in
the systematic way
what if right in examination you write
in triangle abd and triangle EC air what
we see first is angle abd and his angle
V is equal to
and you'll see there is angle ECF right
my angle X is equal to in your legs - or
we can say that he B is equal to e Z in
an agency second thing angle ADB is
equal to angle E FC that is B is equal
to F both on I did it since two angles
are saying in this triangles we can see
that they're both triangle a DP D is
similar to triangle EC by a that's all
let's take this example the question
says side in triangle ABC and PQ our
side ad and BC and the media reading so
if this is X this is y you see this is X
- this is why - - right the question
says side a b and b c or and the median
ad of the triangle ABC you are
proportional to the sides PQ Cuba and
p.m. that is X by X dash is equal to Y
by a y dash is equal to Z by Z - given
also BD is the median that is this is y
by 2 V dy by 2 and this is y dash by
given we have to prove that ABC is
similar to PQ R so to prove ABC is
similar to PQ R we have to option one is
we can either say use saf side angle
side or side side side so if you use
side side side we have to prove that AC
by PR is equal to X - 5 X by X - that is
a little difficult to other option we
have is we have already told X by X dash
is equal to by my eye - if you somehow
prove that angle P is equal to angle Q
if you prove that angle P is equal to
angle QR ratio is short so how to prove
angle B is
if you observe carefully triangle abd
and take em both are similar actually
why the sides are proportional you see
in triangle abd and triangle p qm so
again through both are similar they can
Roop B is equal to so a B is equal to X
P Q is equal to X - 8 is equal to Z this
is equal to Z - this is y by 2 this is a
so we'll divide AV by PQ is equal to X
back - ad by p.m. is equal to Z by Z -
and be D by Q M sorry ad by p.m. is
below self-addressed and BD by Cubans
will do bye bye - bye bye - bye -
boo-boo cancel is equal to Y by Y - and
if you see that we are told that all are
equal X by X dash is equal to Y by Y -
it's alright we are told that they are
equal that means therefore triangle abd
is similar to trying them PQ m in that
case in that case triangle angle abd
this angle B is equal to angle q PQ
correct this is my equation 1 now since
it is equal we can go again in triangle
the bigger triangle a B C and triangle
PQR we see that in y PQ this X by X dash
is equal to VC by QR that is y over y
dash given also angle abd is equal to
angle pqm this way of proof write from
Equation 1 so we can say that therefore
triangle ABC is similar to triangle PQR
how by SAS to sign again side to this
side this angle this sign sign inside
the question says the parameter of two
similar triangles ABC and PQ R so at is
6 and 24 centimeter respectively
because 10 we have to find any so let's
dolls triangle there's two similar
triangles ABC ABC I wrote in the
anti-clockwise fashion 2pq are also
Electra now and it says PQ is 10 we have
to find a way that abbs
since the triangles are similar I can
see that AP by P Q this expert n is
equal to they should the perimeter see
Anthony 180 by bc AP by P Q is equal to
VC by Q R is equal to AC by P R is also
equal to create all this AV plus we feel
blessed easy
my nerves are Nastya but it is 1 by 2
this is 1 by D 1 by 2 this is become 3
by 6 that will also become 1 by 2 my
normal ratio theorem we can see that if
you have PQ is equal to PC by QR is
equal to EC by PR that is also equal to
you add all this you are no this equals
this is nothing but P any meter Oh
triangle ABC this is nothing but AE
meter of triangle PQR correct so we can
see that a vib Q's are the perimeter of
triangle ABC we're trying parameter
pregnant in the winter of triangle ABC
this X by hundred ten is equal to
perimeter of triangle ABC at this 36 and
pqi 24 correct so I will again is x is
nothing 36 in PO's and 10 by 24 well we
to do well in two three fine so this
becomes 15 centimeter so X is 15
centimeter side a B is 15 centimeter
you just use the formula everywhere peak
usable - perimeter of triangle ABC by
trying parameter triangle PQR AV is
equal to x + PQ is equal to 10 all right
parameter of triangle ABC is 36 10 you
know triangle PQR 24 solve this equation
to find x go to 15 centimeter thank you
visit exam viacom to watch free
educational videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thanks again
is brought to you by exam feel calm no
more fear from exam before watching this
video please make sure that you have
watched part 1 to power 25
take for example ABC and EMP our two
right triangles right angle and B at M
respectively you have to prove that
triangle ABC this triangle is similar to
triangle a M so first let us draw this a
b c which one is right triangle ABC like
this let's draw like a we see why
because you see you saw that B is the
right triangle side or like this so true
they were similar I'll draw a similar
triangle like this then also it will be
right triangle it should be empty why
because it is ABC and a MP mayrose if
you see any right right now to prove
they're similar first thing is these to
hang over scene done deal and if we can
prove that with an angular same audition
so on so if you see the angle ABC this
triangle right triangle a MP this
triangle right angle a is common so
angle a is equal to angle a now since we
have seen that what if I got a similar
let's write the steps step says in
triangle B AC and triangle M AP all
right angle BAC is equal to angle M AP y
same angle or you can write by
construction also an angle ABC is equal
to angle a empty y 90 degree therefore
these two angles are equal we can say
that triangle V is similar to triangle m
AP so let's take number problem the
question says E is a point on side C be
produced of an isosceles triangle ABC
with a B is equal to EC a B is equal to
BC this is a side CB produced this is
the point II a name is equal to AC ad is
parallel to BC and he gave his pattern
to AC you have to prove that triangle
abd is similar to EFC so we see abd this
is 90 so we draw a triangle like this
it's cut this this is one triangle this
is one triangle a B D D is 90 degree we
can see AV e sempre triangle abd is
similar to EF CBO to prove that this is
e this is f this is e CF son EC EC and
has two identity and if you see M is 90
not to prove both the triangles are
similar
first thing is angle D is equal to angle
F dot d with a 90 now we have to prove
either a is equal to e or B is equal to
C if you prove any of this are polymers
so on see first thing that comes to our
mind when I can we say a B is equal to
EC that is both hangers are similar so
this is left repose X so this becomes X
- that makes simple to angle X - helix
into English - why because a B is equal
to H now if you see in triangle be a D
angle B is X and angle C EF c EF angle C
is go to X dash and here is our solution
Phi because is X equal to X dash we can
see that angle B is good doing a see D
is equal to f is already put with 90 so
they are similar so now let us write in
the systematic way
what if right in examination you write
in triangle abd and triangle EC air what
we see first is angle abd and his angle
V is equal to
and you'll see there is angle ECF right
my angle X is equal to in your legs - or
we can say that he B is equal to e Z in
an agency second thing angle ADB is
equal to angle E FC that is B is equal
to F both on I did it since two angles
are saying in this triangles we can see
that they're both triangle a DP D is
similar to triangle EC by a that's all
let's take this example the question
says side in triangle ABC and PQ our
side ad and BC and the media reading so
if this is X this is y you see this is X
- this is why - - right the question
says side a b and b c or and the median
ad of the triangle ABC you are
proportional to the sides PQ Cuba and
p.m. that is X by X dash is equal to Y
by a y dash is equal to Z by Z - given
also BD is the median that is this is y
by 2 V dy by 2 and this is y dash by
given we have to prove that ABC is
similar to PQ R so to prove ABC is
similar to PQ R we have to option one is
we can either say use saf side angle
side or side side side so if you use
side side side we have to prove that AC
by PR is equal to X - 5 X by X - that is
a little difficult to other option we
have is we have already told X by X dash
is equal to by my eye - if you somehow
prove that angle P is equal to angle Q
if you prove that angle P is equal to
angle QR ratio is short so how to prove
angle B is
if you observe carefully triangle abd
and take em both are similar actually
why the sides are proportional you see
in triangle abd and triangle p qm so
again through both are similar they can
Roop B is equal to so a B is equal to X
P Q is equal to X - 8 is equal to Z this
is equal to Z - this is y by 2 this is a
so we'll divide AV by PQ is equal to X
back - ad by p.m. is equal to Z by Z -
and be D by Q M sorry ad by p.m. is
below self-addressed and BD by Cubans
will do bye bye - bye bye - bye -
boo-boo cancel is equal to Y by Y - and
if you see that we are told that all are
equal X by X dash is equal to Y by Y -
it's alright we are told that they are
equal that means therefore triangle abd
is similar to trying them PQ m in that
case in that case triangle angle abd
this angle B is equal to angle q PQ
correct this is my equation 1 now since
it is equal we can go again in triangle
the bigger triangle a B C and triangle
PQR we see that in y PQ this X by X dash
is equal to VC by QR that is y over y
dash given also angle abd is equal to
angle pqm this way of proof write from
Equation 1 so we can say that therefore
triangle ABC is similar to triangle PQR
how by SAS to sign again side to this
side this angle this sign sign inside
the question says the parameter of two
similar triangles ABC and PQ R so at is
6 and 24 centimeter respectively
because 10 we have to find any so let's
dolls triangle there's two similar
triangles ABC ABC I wrote in the
anti-clockwise fashion 2pq are also
Electra now and it says PQ is 10 we have
to find a way that abbs
since the triangles are similar I can
see that AP by P Q this expert n is
equal to they should the perimeter see
Anthony 180 by bc AP by P Q is equal to
VC by Q R is equal to AC by P R is also
equal to create all this AV plus we feel
blessed easy
my nerves are Nastya but it is 1 by 2
this is 1 by D 1 by 2 this is become 3
by 6 that will also become 1 by 2 my
normal ratio theorem we can see that if
you have PQ is equal to PC by QR is
equal to EC by PR that is also equal to
you add all this you are no this equals
this is nothing but P any meter Oh
triangle ABC this is nothing but AE
meter of triangle PQR correct so we can
see that a vib Q's are the perimeter of
triangle ABC we're trying parameter
pregnant in the winter of triangle ABC
this X by hundred ten is equal to
perimeter of triangle ABC at this 36 and
pqi 24 correct so I will again is x is
nothing 36 in PO's and 10 by 24 well we
to do well in two three fine so this
becomes 15 centimeter so X is 15
centimeter side a B is 15 centimeter
you just use the formula everywhere peak
usable - perimeter of triangle ABC by
trying parameter triangle PQR AV is
equal to x + PQ is equal to 10 all right
parameter of triangle ABC is 36 10 you
know triangle PQR 24 solve this equation
to find x go to 15 centimeter thank you
visit exam viacom to watch free
educational videos try free online tests
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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