Class 6 Exam > Class 6 Videos > Mathematics (Maths) Class 6 > Examples: Curve, Angles
Examples: Curve, Angles Video Lecture | Mathematics (Maths) Class 6
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FAQs on Examples: Curve, Angles Video Lecture - Mathematics (Maths) Class 6
| 1. What is a curve in mathematics? |  |
Ans. In mathematics, a curve is a continuous and smooth line that does not have any sharp corners or edges. It can be represented by a mathematical equation or graph. Curves can be open or closed, and they can vary in shape and size.
| 2. How are curves different from straight lines? | |
Ans. Unlike straight lines that have a constant slope, curves in mathematics have a changing slope at different points. Curves can bend and change direction, while straight lines remain constant in their direction. Additionally, curves can have different curvatures and shapes, such as parabolic, circular, or elliptical.
| 3. What is an angle in mathematics? | |
Ans. In mathematics, an angle is a figure formed by two rays or line segments that share a common endpoint called the vertex. Angles are measured in degrees and can range from 0 to 360 degrees. They are used to measure the amount of rotation or inclination between two lines or planes.
| 4. How do you classify angles? | |
Ans. Angles can be classified based on their measurements. Some common classifications of angles include:
- Acute angle: An angle that measures less than 90 degrees.
- Right angle: An angle that measures exactly 90 degrees.
- Obtuse angle: An angle that measures more than 90 degrees but less than 180 degrees.
- Straight angle: An angle that measures exactly 180 degrees.
- Reflex angle: An angle that measures more than 180 degrees but less than 360 degrees.
| 5. How do angles and curves relate to each other? | |
Ans. Angles and curves are interconnected in geometry. When a curve changes direction, it forms an angle at the point of curvature. The size of the angle depends on the sharpness or smoothness of the curve. Angles are also used to measure the inclination or slope of a curve at a specific point. In geometric shapes, angles are formed at the intersections of lines or curves, determining their overall properties and relationships.
Text Transcript from Video
hello friends this video on basic
geometrical ideas part 16 is brought to
you by exam for calm no more fear from
exam so based on whatever we have
studied so far because we have learned a
lot of new things we learnt about angles
we learnt about polygons we learned
about closed curves so let us quickly
try to look at some of the questions
just to ensure that our understanding is
correct so let us look at question
number 1 in the given diagram name the
point in that interior of angle D o e so
when you look at angle D oh so this is
the angle that we are talking about so
which portion will be the interior of
this angle the portion which is enclosed
by the two arms of the angle so
basically this entire portion would be
the interior of this angle so is there
any point which lies in this portion yes
of course there is this point in so the
point that lies in the interior of angle
D OE is a in the exterior of angle e o F
where is a o f this is e o F so exterior
of ego f so what would the exterior of a
oh and anything which is outside yo f
right so this this area would be the
interior of ego F right so what is
outside anything outside this would be
outside in fact this point a which was
in the interior of I will do e is
exterior of angle e o F because it is
outside of ego F so point E is one such
point is there any other point which is
located outside angle vo f of course
there is this point C so C is also
outside of angle ego F can you see any
other point which is located outside of
ego F what about this point B because D
is also located outside this angle and D
is no way related to this angle
so be is also another point which is in
the exterior of angle E or F or angle E
Oh F now on that means it is neither
inside not outside it is on the boundary
so let us look at how will e Oh F so do
you see any point which is located on
the arm of the EOS angle of course there
is this point B because b is located on
the arm
e o so therefore B is one such point
which is located on the arm of angle e
Oh F
other than B do you have any other point
which is located on angle here F of
course e oh if they these are the points
which are themselves located on the
angle right because they offer is the
vertex E if they are located on the
reefs which form the angle therefore e o
FB these are all located on angle cos
question number two name the angles in
the given figure so here how many angles
do you see so let's discuss a few more
things do you think this is a polygon
yes because it is made up of four line
segments 80 BC CB and BA so how many
angles are involved one two three and
four so can we name these angles let's
start with this angle so every time we
name an angle we always put the vertex
in between so this angle the vertex is a
so a will be in between and this would
be PAP the next angle angle D so T is
the vertex so B will be in between and
this would be a DC for this angle C
should be in between and the angle
should be dece B and for this angle D
should be in between and the name should
be C B a so these are the angles in this
figure question number three draw
diagrams of two angles such that they
have one point in common so let us try
to draw such two angles so let us see so
we will just draw a rough diagrams here
so let us say we draw angles in this way
let's say this is one angle this is
another angle so which is the common
point this is the common point so let us
call this point as P this as a this is C
this is e and this is d so angle ABC and
angle eb d they have one point in common
and that common point is B so this was
first second has two points in common so
let us try to draw a slightly different
diagram so let's say this is point a
this is point B this is point D this is
Point C so when you look at this angle
angle ABC and if you look at angle CBA
what you see you have two points in
common and what are those two common
points B and C similarly three points in
common so how can you have two angles
with three points in common so in your
in fact we can do it in the very same
figure also so in this figure itself
let's see if you have another point here
called point II if you keep on adding
more number of points here so you can
actually get more common points which
would be common between these two angles
because these points would lie on both
the angles right number D one way in
common so there also I think we can make
use of the same figure but anyways we
draw another figure select C you draw a
figure like this let's call this B this
is a this is D and this is C so when you
look at these two angles and then see a
D and angle B ad so ad is a common rail
so ad is the common ring so in this way
we can draw these rough diagrams with
common points and
raise between two angles question number
four classify the following curves as
open or closed now how do we determine
which is an open curve and which is a
closed curve then open curve will always
have a fixed starting point and a fixed
ending point and if this would and that
open curve would not enclose a space
within so let us look at each of these
first one you have its definite starting
point and ending point then it the start
point in the end point you do not meet
therefore this is an open curve look at
this one can you tell me which is the
starting point we do not know because
you see it is closed from everywhere and
it encloses a space within it so this
space is actually enclosed by this curve
so that tells us that this is a closed
curve look at this here you have a
distinct start point and a distinct end
point so here again you do not have an
enclosed area as such you cannot call
this as enclosed area because here from
here it is open so you do not know till
there it is enclosed so basically this
is also an open curve this one is
definitely a closed curve because it is
closed from all ends and we do not know
from where it started and from where it
ended this one is also a closed curve in
fact these two they are actually
polygons because they are closed curves
made up of line segments question number
five draw any polygon and shade its
interior that that's quite simple so
what does a polygon it is a closed curve
which is made up of only line segments
so you can draw as many line segments as
you want but end of it it should be a
closed curve that is there should be no
start point no end point and then the
interior would be the area enclosed by
the polygon so this is how you can shade
the ingredient question number six
consider the given figure and answer the
questions is it a curve is it closed now
when you look at this
diagram what do you think is it a curve
of course it is a curve because how do
we define a curve is it all this curve
is something which is not straight do
you think it is straight this is not
straight because a straight line would
be something like this
but is it straight it is not straight
because it is made up of many line
segments and overall the outline is not
straight so therefore this is a curve of
course it is a curve and is it closed of
course it is closed because we cannot
see the start point and end point
instead we can see that it encloses an
area within it so this is the enclosed
area inside so definitely this is a
closed curve question number seven
illustrate if possible each one of the
following with a rough diagram a closed
curve that is not a polygon now can you
have a closed curve which is not a
polygon is of course you can have one
because in order to become a polygon the
closed curve should be made up of only
line segments but if we have a closed
curve like this this is also closed
curve but this is not a polygon second
one an open curve made up entirely of
line segments yes that is also possible
so you keep drawing a curve with as many
line segments as you want and then you
leave it like this so in this case you
have a start point you have an end point
and you see that it is open it is not
closed he doesn't encloses a region
within it so therefore this is open
curve but it is made up of line segments
see a polygon with two sides this is not
possible so if you have two sides you
can never get a closed curve so no
matter however hard you try to make
these two straight lines that is two
line segments join now the moment you
want to join to lie
segments you have to bank their
blindness at the moment you bind them
they are no more line segments they
become curved so therefore this is never
possible so this to draw a polygon with
two sides is not possible thank you
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daily updates thank you
geometrical ideas part 16 is brought to
you by exam for calm no more fear from
exam so based on whatever we have
studied so far because we have learned a
lot of new things we learnt about angles
we learnt about polygons we learned
about closed curves so let us quickly
try to look at some of the questions
just to ensure that our understanding is
correct so let us look at question
number 1 in the given diagram name the
point in that interior of angle D o e so
when you look at angle D oh so this is
the angle that we are talking about so
which portion will be the interior of
this angle the portion which is enclosed
by the two arms of the angle so
basically this entire portion would be
the interior of this angle so is there
any point which lies in this portion yes
of course there is this point in so the
point that lies in the interior of angle
D OE is a in the exterior of angle e o F
where is a o f this is e o F so exterior
of ego f so what would the exterior of a
oh and anything which is outside yo f
right so this this area would be the
interior of ego F right so what is
outside anything outside this would be
outside in fact this point a which was
in the interior of I will do e is
exterior of angle e o F because it is
outside of ego F so point E is one such
point is there any other point which is
located outside angle vo f of course
there is this point C so C is also
outside of angle ego F can you see any
other point which is located outside of
ego F what about this point B because D
is also located outside this angle and D
is no way related to this angle
so be is also another point which is in
the exterior of angle E or F or angle E
Oh F now on that means it is neither
inside not outside it is on the boundary
so let us look at how will e Oh F so do
you see any point which is located on
the arm of the EOS angle of course there
is this point B because b is located on
the arm
e o so therefore B is one such point
which is located on the arm of angle e
Oh F
other than B do you have any other point
which is located on angle here F of
course e oh if they these are the points
which are themselves located on the
angle right because they offer is the
vertex E if they are located on the
reefs which form the angle therefore e o
FB these are all located on angle cos
question number two name the angles in
the given figure so here how many angles
do you see so let's discuss a few more
things do you think this is a polygon
yes because it is made up of four line
segments 80 BC CB and BA so how many
angles are involved one two three and
four so can we name these angles let's
start with this angle so every time we
name an angle we always put the vertex
in between so this angle the vertex is a
so a will be in between and this would
be PAP the next angle angle D so T is
the vertex so B will be in between and
this would be a DC for this angle C
should be in between and the angle
should be dece B and for this angle D
should be in between and the name should
be C B a so these are the angles in this
figure question number three draw
diagrams of two angles such that they
have one point in common so let us try
to draw such two angles so let us see so
we will just draw a rough diagrams here
so let us say we draw angles in this way
let's say this is one angle this is
another angle so which is the common
point this is the common point so let us
call this point as P this as a this is C
this is e and this is d so angle ABC and
angle eb d they have one point in common
and that common point is B so this was
first second has two points in common so
let us try to draw a slightly different
diagram so let's say this is point a
this is point B this is point D this is
Point C so when you look at this angle
angle ABC and if you look at angle CBA
what you see you have two points in
common and what are those two common
points B and C similarly three points in
common so how can you have two angles
with three points in common so in your
in fact we can do it in the very same
figure also so in this figure itself
let's see if you have another point here
called point II if you keep on adding
more number of points here so you can
actually get more common points which
would be common between these two angles
because these points would lie on both
the angles right number D one way in
common so there also I think we can make
use of the same figure but anyways we
draw another figure select C you draw a
figure like this let's call this B this
is a this is D and this is C so when you
look at these two angles and then see a
D and angle B ad so ad is a common rail
so ad is the common ring so in this way
we can draw these rough diagrams with
common points and
raise between two angles question number
four classify the following curves as
open or closed now how do we determine
which is an open curve and which is a
closed curve then open curve will always
have a fixed starting point and a fixed
ending point and if this would and that
open curve would not enclose a space
within so let us look at each of these
first one you have its definite starting
point and ending point then it the start
point in the end point you do not meet
therefore this is an open curve look at
this one can you tell me which is the
starting point we do not know because
you see it is closed from everywhere and
it encloses a space within it so this
space is actually enclosed by this curve
so that tells us that this is a closed
curve look at this here you have a
distinct start point and a distinct end
point so here again you do not have an
enclosed area as such you cannot call
this as enclosed area because here from
here it is open so you do not know till
there it is enclosed so basically this
is also an open curve this one is
definitely a closed curve because it is
closed from all ends and we do not know
from where it started and from where it
ended this one is also a closed curve in
fact these two they are actually
polygons because they are closed curves
made up of line segments question number
five draw any polygon and shade its
interior that that's quite simple so
what does a polygon it is a closed curve
which is made up of only line segments
so you can draw as many line segments as
you want but end of it it should be a
closed curve that is there should be no
start point no end point and then the
interior would be the area enclosed by
the polygon so this is how you can shade
the ingredient question number six
consider the given figure and answer the
questions is it a curve is it closed now
when you look at this
diagram what do you think is it a curve
of course it is a curve because how do
we define a curve is it all this curve
is something which is not straight do
you think it is straight this is not
straight because a straight line would
be something like this
but is it straight it is not straight
because it is made up of many line
segments and overall the outline is not
straight so therefore this is a curve of
course it is a curve and is it closed of
course it is closed because we cannot
see the start point and end point
instead we can see that it encloses an
area within it so this is the enclosed
area inside so definitely this is a
closed curve question number seven
illustrate if possible each one of the
following with a rough diagram a closed
curve that is not a polygon now can you
have a closed curve which is not a
polygon is of course you can have one
because in order to become a polygon the
closed curve should be made up of only
line segments but if we have a closed
curve like this this is also closed
curve but this is not a polygon second
one an open curve made up entirely of
line segments yes that is also possible
so you keep drawing a curve with as many
line segments as you want and then you
leave it like this so in this case you
have a start point you have an end point
and you see that it is open it is not
closed he doesn't encloses a region
within it so therefore this is open
curve but it is made up of line segments
see a polygon with two sides this is not
possible so if you have two sides you
can never get a closed curve so no
matter however hard you try to make
these two straight lines that is two
line segments join now the moment you
want to join to lie
segments you have to bank their
blindness at the moment you bind them
they are no more line segments they
become curved so therefore this is never
possible so this to draw a polygon with
two sides is not possible thank you
please visit exam fee or come for free
quality education you can learn with a
simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class six to
twelve on physics chemistry mathematics
and biology along with practical videos
so please subscribe to our channel for
daily updates thank you
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Dec 26, 2024 Last updated |
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