Class 10 Exam > Class 10 Videos > L15 : Examples Angle Bisector-3 - Triangles, Maths, Class 10
L15 : Examples Angle Bisector-3 - Triangles, Maths, Class 10 Video Lecture
FAQs on L15 : Examples Angle Bisector-3 - Triangles, Maths, Class 10 Video Lecture
| 1. What is an angle bisector? |  |
Ans. An angle bisector is a line or ray that divides an angle into two equal parts. It passes through the vertex of the angle and divides it into two congruent angles.
| 2. How do you construct an angle bisector? | |
Ans. To construct an angle bisector, follow these steps:
1. Draw the given angle.
2. Place the compass on the vertex of the angle and draw an arc that intersects both sides of the angle.
3. Without changing the compass width, place the compass on the points where the arc intersects the sides of the angle and draw two arcs that intersect each other.
4. Draw a line segment connecting the vertex of the angle to the point where the two arcs intersect. This line segment is the angle bisector.
| 3. What is the importance of angle bisectors in triangles? | |
Ans. Angle bisectors have several important properties in triangles:
- The angle bisectors of a triangle intersect at a point called the incenter, which is equidistant from the sides of the triangle.
- The incenter is the center of the inscribed circle within the triangle.
- The angle bisector theorem states that the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the lengths of the other two sides.
| 4. How are angle bisectors used in real-life applications? | |
Ans. Angle bisectors have practical applications in various fields, including:
- Architecture and construction: Angle bisectors help in determining the correct angles for building structures and ensuring stability.
- Navigation: Angle bisectors are used in navigation systems to calculate accurate directions and angles for ships, aircraft, and vehicles.
- Surveying: Angle bisectors assist surveyors in accurately measuring angles and determining land boundaries.
- Engineering: Angle bisectors are used in engineering designs and calculations for various structures, such as bridges and buildings.
| 5. Can angle bisectors be used to find the lengths of sides in a triangle? | |
Ans. No, angle bisectors alone cannot be used to find the lengths of sides in a triangle. However, the angle bisector theorem can be used in combination with other geometric properties to determine the lengths of sides. The theorem states that the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the lengths of the other two sides. By using this theorem and additional measurements or ratios, the lengths of sides can be calculated.
Text Transcript from Video
hello friends this video on triangles
part 15 is brought you by exams here
calm no more fear from exam before
watching this video please make sure
that you have watched part 1 - part 14
take from my example 80 is the median
and V E and F are bisectors of angle ADB
and ADC meet a B and a C in E and a
perspectively we have to prove that is
parallel to BC let's do this this is the
triangle and this is ABC so we have this
triangle ABC now let's draw a G why
because ad is the median so this ad is
the median now we equal we go to DC
correct right because ad is a median
second thing potion says is that de and
EF are bisectors of angle ADB and a DC
so ad because this triangle this angle
and D is a bicycle so let's draw this
bicycle so this is VC correctly so
second thing is DF is the bisector of
this angle this angle that is a DC the
bisector is DF so let's draw this angle
so DF is a bisector of the sign and just
looking at E and F perspective we have
to prove that EF is parallel to BC so
let's draw here this is VA and we have
to prove EA this volatility so what we
are told if this is 1 this become one -
this is 2 this become - so we are told
that angle 1 is equal to m1 -
correct angle is equal to make them too
- although we are told that
BD is equal to BC this is something that
is given to us correct
now we'll start on now the question is
how to approach here also if you see we
are asked to prove EF is parallel to BC
if we can prove that a by EB is equal to
EA by RC
so let's suppose this is X this is y
this is X dash y dash so if we can prove
that X by Y is equal to X attacked by my
- Parkinson if X by Y is good to egg to
the bye - then we can say that he is
parallel to BC correct so let's do this
if you see X by Y let's see what is the
value of x by Y so X by Y is nothing but
8 by BD y because angle 1 is written
like the production since he is the
bisector of angle ADB and you see that X
by y is equal to 80 by BD similarly X -
bye-bye - is nothing but a D by DZ why
because they get to this red triangle -
- that is DFS bisector of angle ADC
CPA about X bye-bye everyone X is
invited
we also know that DC is equal to BD
correct so I can rewrite this as 80 by V
so if you see the right-hand side of
this is equal to this so I can say that
so merge these two equations is equation
1 let's suppose this is equation 2 I can
say that X by y is equal to 80 by D D is
equal to 80 so - or I can say that X by
a Y is equal to English bye-bye - so if
X by y is equal to X dividers this
implies that EF is parallel to BC
correct
we are told add power line there is a
parallel line intersects the sides
proportionally so if a by EB is equal to
VF by FC that means
EF is power I do is let us say for
example in triangle ABC D is the
midpoint of BC and PD is a bisector of
angle ADB and he is this drawn parallel
to BC cut it easy now we have to
prove that EDM is right now everything
is Omega so now let's draw the triangle
this is the triangle let's name it ABC
right this is we have done this is
really an ABC with triangle B of them D
is the midpoint of BC so let us take
this D these are a point of e C this is
also that it is the bisector of angle a
bb8 DV is this one so let us draw this
we have a degree now this is Michael EDB
PD is a bisector of this so just already
this is me that means this is 1 and this
is 1 - correct because it is a bisector
of angle a TV done he has drawn parallel
to BC still have strong EF palette to be
seen sit on palliative busy so I'll mark
like this EF is parallel to BC and this
is their correct he F is non Catholic -
we see cutting easy we have to prove
that even f e DF is a right so to prove
it here this right triangle X draw this
DM because nobody will get median this
is livia you have to prove that he did
here this right right correct so what we
can do here - this X so we have to prove
that - 1 plus X is a little do you also
know that if this is the X this is 1
let's suppose this body we know that 1
plus 1 dash plus X plus y is equal to
180 correct
straight line 1 is equal to 1 - I said -
into angle 1 plus X plus y is equal to
yd now I have to prove that angle 1 plus
X is equal to 90 so if I just if I'm
able to prove an X into y in that case
one cuz I should be 90
because 1 plus X 90 and this one that is
all right
so you can show you don't know I guess
so that into angle 1 plus X plus y is
equal to 180
if I can prove it X got to Y then this
will become 2 into 1 1 plus 2 into angle
X is equal to 180 or angle 1 plus angle
X 90 you can improve that x squared - y
that means I can prove that EDM is right
just approach so one approach for to
solve this question so you can prove
that X equal to Y that desire to prove
that FD is an angle bisector of anything
try to prove that I have to prove that
ad by DC's you can do AF pi FC the
reverse is ring approach right now if
you know that am IFC's you can do any PI
PC because he is parallel to BC correct
now with this by this is equal to this
by this and this by the Beatles you can
prove that so let's try so given is
right given given is VDD is equal to DZ
first thing then given angle 1 is equal
to angle 1 - and EF is parallel to BC to
prove that X is a little boy I'm Alexa
bit alike otherwise if you do this then
we can prove that 1 plus X been to 90
degree so if we prove this to prove this
let's go buy a reverse getting a potion
let's assume this is e this is V length
oh this is this will be in action
this is we - so first thing that comes
to our mind is an EF is parallel to BC
is a by B
- I agree - right why so EF is valid to
BC now we have to prove that somehow
that ad by d C is equal to a - - we have
to prove this so let's go buy a reverse
engineering method a by PE is also equal
to ad by VD correct right I'll tell you
why because angle one is where -
Magneton - so this angle one is going to
enter one man that me series the
bisector of angle ADB so I can say that
a by P is equal to 80 by BD
now since B is equal to BC I can say
that this is nothing but a dy DZ right
because we D is going to be Z even now I
know that a by B is equal to 80 by this
alright also a by B is nothing but it
has hit me - this is nothing but a D by
D C now when I say that a d by DZ is
equal to 8 as a V - that means from this
we can conclude that angle X is 1 Y
because if a DT by DZ is equal to a - V
- this EF by FC we can say that DF is
the angle bisector of angle ABC so angle
X is going to make them since the Apple
in the legs Pinto egged Y so this is
angle X mom so total angle I have it is
angled 1 plus angle 1 - so I guess a
angle one only because one is good 2 1
dash plus all it related here see since
we see the straight line I can see that
angle 1 dash plus angle 1 plus X plus
is equal to 180 correctly I got one -
equal do I kill one only instance from
single one plus angle 1 plus X Y is also
equal to X mu G context but alright but
I can say that to mean - angle 1 plus X
this is equal to 180 or what I get is
again 1 plus X equal to what I do I do
that is 90 degree and that is what I was
supposed to move that is angle 1 plus X
that is angle e DF is 90 the approach I
followed was I went by a reversal method
I observed that if I can prove that this
is angle X is equal to again why my
problem is solved and to prove that I
was supposed to prove that he is my
angle bisector of a DC that is ad by DT
should be equal to a dash line drive
thank you visit exam viacom to watch
free education videos try free online
test get the best quality study
materials study from the best tutors and
mentors and mass flow thanks all scream
part 15 is brought you by exams here
calm no more fear from exam before
watching this video please make sure
that you have watched part 1 - part 14
take from my example 80 is the median
and V E and F are bisectors of angle ADB
and ADC meet a B and a C in E and a
perspectively we have to prove that is
parallel to BC let's do this this is the
triangle and this is ABC so we have this
triangle ABC now let's draw a G why
because ad is the median so this ad is
the median now we equal we go to DC
correct right because ad is a median
second thing potion says is that de and
EF are bisectors of angle ADB and a DC
so ad because this triangle this angle
and D is a bicycle so let's draw this
bicycle so this is VC correctly so
second thing is DF is the bisector of
this angle this angle that is a DC the
bisector is DF so let's draw this angle
so DF is a bisector of the sign and just
looking at E and F perspective we have
to prove that EF is parallel to BC so
let's draw here this is VA and we have
to prove EA this volatility so what we
are told if this is 1 this become one -
this is 2 this become - so we are told
that angle 1 is equal to m1 -
correct angle is equal to make them too
- although we are told that
BD is equal to BC this is something that
is given to us correct
now we'll start on now the question is
how to approach here also if you see we
are asked to prove EF is parallel to BC
if we can prove that a by EB is equal to
EA by RC
so let's suppose this is X this is y
this is X dash y dash so if we can prove
that X by Y is equal to X attacked by my
- Parkinson if X by Y is good to egg to
the bye - then we can say that he is
parallel to BC correct so let's do this
if you see X by Y let's see what is the
value of x by Y so X by Y is nothing but
8 by BD y because angle 1 is written
like the production since he is the
bisector of angle ADB and you see that X
by y is equal to 80 by BD similarly X -
bye-bye - is nothing but a D by DZ why
because they get to this red triangle -
- that is DFS bisector of angle ADC
CPA about X bye-bye everyone X is
invited
we also know that DC is equal to BD
correct so I can rewrite this as 80 by V
so if you see the right-hand side of
this is equal to this so I can say that
so merge these two equations is equation
1 let's suppose this is equation 2 I can
say that X by y is equal to 80 by D D is
equal to 80 so - or I can say that X by
a Y is equal to English bye-bye - so if
X by y is equal to X dividers this
implies that EF is parallel to BC
correct
we are told add power line there is a
parallel line intersects the sides
proportionally so if a by EB is equal to
VF by FC that means
EF is power I do is let us say for
example in triangle ABC D is the
midpoint of BC and PD is a bisector of
angle ADB and he is this drawn parallel
to BC cut it easy now we have to
prove that EDM is right now everything
is Omega so now let's draw the triangle
this is the triangle let's name it ABC
right this is we have done this is
really an ABC with triangle B of them D
is the midpoint of BC so let us take
this D these are a point of e C this is
also that it is the bisector of angle a
bb8 DV is this one so let us draw this
we have a degree now this is Michael EDB
PD is a bisector of this so just already
this is me that means this is 1 and this
is 1 - correct because it is a bisector
of angle a TV done he has drawn parallel
to BC still have strong EF palette to be
seen sit on palliative busy so I'll mark
like this EF is parallel to BC and this
is their correct he F is non Catholic -
we see cutting easy we have to prove
that even f e DF is a right so to prove
it here this right triangle X draw this
DM because nobody will get median this
is livia you have to prove that he did
here this right right correct so what we
can do here - this X so we have to prove
that - 1 plus X is a little do you also
know that if this is the X this is 1
let's suppose this body we know that 1
plus 1 dash plus X plus y is equal to
180 correct
straight line 1 is equal to 1 - I said -
into angle 1 plus X plus y is equal to
yd now I have to prove that angle 1 plus
X is equal to 90 so if I just if I'm
able to prove an X into y in that case
one cuz I should be 90
because 1 plus X 90 and this one that is
all right
so you can show you don't know I guess
so that into angle 1 plus X plus y is
equal to 180
if I can prove it X got to Y then this
will become 2 into 1 1 plus 2 into angle
X is equal to 180 or angle 1 plus angle
X 90 you can improve that x squared - y
that means I can prove that EDM is right
just approach so one approach for to
solve this question so you can prove
that X equal to Y that desire to prove
that FD is an angle bisector of anything
try to prove that I have to prove that
ad by DC's you can do AF pi FC the
reverse is ring approach right now if
you know that am IFC's you can do any PI
PC because he is parallel to BC correct
now with this by this is equal to this
by this and this by the Beatles you can
prove that so let's try so given is
right given given is VDD is equal to DZ
first thing then given angle 1 is equal
to angle 1 - and EF is parallel to BC to
prove that X is a little boy I'm Alexa
bit alike otherwise if you do this then
we can prove that 1 plus X been to 90
degree so if we prove this to prove this
let's go buy a reverse getting a potion
let's assume this is e this is V length
oh this is this will be in action
this is we - so first thing that comes
to our mind is an EF is parallel to BC
is a by B
- I agree - right why so EF is valid to
BC now we have to prove that somehow
that ad by d C is equal to a - - we have
to prove this so let's go buy a reverse
engineering method a by PE is also equal
to ad by VD correct right I'll tell you
why because angle one is where -
Magneton - so this angle one is going to
enter one man that me series the
bisector of angle ADB so I can say that
a by P is equal to 80 by BD
now since B is equal to BC I can say
that this is nothing but a dy DZ right
because we D is going to be Z even now I
know that a by B is equal to 80 by this
alright also a by B is nothing but it
has hit me - this is nothing but a D by
D C now when I say that a d by DZ is
equal to 8 as a V - that means from this
we can conclude that angle X is 1 Y
because if a DT by DZ is equal to a - V
- this EF by FC we can say that DF is
the angle bisector of angle ABC so angle
X is going to make them since the Apple
in the legs Pinto egged Y so this is
angle X mom so total angle I have it is
angled 1 plus angle 1 - so I guess a
angle one only because one is good 2 1
dash plus all it related here see since
we see the straight line I can see that
angle 1 dash plus angle 1 plus X plus
is equal to 180 correctly I got one -
equal do I kill one only instance from
single one plus angle 1 plus X Y is also
equal to X mu G context but alright but
I can say that to mean - angle 1 plus X
this is equal to 180 or what I get is
again 1 plus X equal to what I do I do
that is 90 degree and that is what I was
supposed to move that is angle 1 plus X
that is angle e DF is 90 the approach I
followed was I went by a reversal method
I observed that if I can prove that this
is angle X is equal to again why my
problem is solved and to prove that I
was supposed to prove that he is my
angle bisector of a DC that is ad by DT
should be equal to a dash line drive
thank you visit exam viacom to watch
free education videos try free online
test get the best quality study
materials study from the best tutors and
mentors and mass flow thanks all scream
About this Video
Sep 05, 2025
Last updated
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