Class 8 Exam > Class 8 Videos > L21 : Questions-8 - Quadrilaterals , Maths, Class 8
L21 : Questions-8 - Quadrilaterals , Maths, Class 8 Video Lecture
FAQs on L21 : Questions-8 - Quadrilaterals , Maths, Class 8 Video Lecture
| 1. What are the properties of a quadrilateral? |  |
Ans. A quadrilateral is a polygon with four sides. The properties of a quadrilateral include:
- It has four vertices and four angles.
- The sum of its interior angles is always 360 degrees.
- Its opposite sides are parallel.
- Its opposite angles are equal.
- The sum of the lengths of any two sides is always greater than the lengths of the other two sides.
| 2. What are the different types of quadrilaterals? | |
Ans. There are several types of quadrilaterals, including:
- Parallelogram: A quadrilateral with opposite sides parallel.
- Rectangle: A quadrilateral with four right angles.
- Square: A quadrilateral with four equal sides and four right angles.
- Rhombus: A quadrilateral with four equal sides.
- Trapezoid: A quadrilateral with one pair of parallel sides.
- Kite: A quadrilateral with two pairs of adjacent sides that are equal.
| 3. How do you find the area of a quadrilateral? | |
Ans. The formula to find the area of a quadrilateral depends on its type:
- For a parallelogram, the area is given by the product of its base and height.
- For a rectangle, the area is given by the product of its length and width.
- For a square, the area is given by the square of its side length.
- For a rhombus, the area is given by the product of its diagonals divided by 2.
- For a trapezoid, the area is given by the average of its bases multiplied by its height.
- For a kite, the area is given by the product of its diagonals divided by 2.
| 4. What is the difference between a quadrilateral and a polygon? | |
Ans. A quadrilateral is a specific type of polygon. While all quadrilaterals are polygons, not all polygons are quadrilaterals. A polygon is any closed figure with three or more straight sides, while a quadrilateral specifically refers to a polygon with four sides.
| 5. How do you determine if a quadrilateral is a parallelogram? | |
Ans. To determine if a quadrilateral is a parallelogram, you can use the following criteria:
- If both pairs of opposite sides are parallel, it is a parallelogram.
- If both pairs of opposite angles are equal, it is a parallelogram.
- If one pair of opposite sides is parallel and equal, it is a parallelogram.
- If the diagonals bisect each other, it is a parallelogram.
- If one pair of opposite angles is supplementary (their sum is 180 degrees), it is a parallelogram.
Text Transcript from Video
hello friends this video on
quadrilaterals 521 is brought to you by
exam feel calm no more fear from exam
for right angles now when you talk about
quadrilaterals with all sides equal so
all that we can think of the first thing
that comes to our mind is a square where
all sides are equal and all angles are
also equal so basically square would
come here also because in square you
have all right angles so square would
fit into this criteria as well four
sides equal another example would be
rhombus in rhombus also we have four
sides equal but in this case the angles
are not equal now when you talk about
four right angles one two could be
square the other could be rectangle
where all the angles and height angles
but their sides are not equal question
number three name the quadrilaterals
whose diagonals bisect each other now
there are many such quadrilaterals one
such quadrilateral is a parallelogram so
imperil you blame the diagonals bisect
each other you think of the special
parallelograms and they also come under
spiral Oh Graham anyways because all the
tangles are parallelogram all squares
are also parallelogram all rhombuses are
also parallelogram so parallelograms
articles where the diagonals bisect each
other where diagonals are perpendicular
bisectors of each other so this happens
only in case of square and rhombus
diagonals are equal diagonals are equal
this happens again in piece of square
and rectangle so we have proved each of
these properties in detail some time
back so I think you can refer them if
you want to know why this happens
question number four ABC is a
right-angled triangle and O is the
midpoint of the side opposite to the
right angle so right and
this angle that will be so AC is the
side opposite to the right angle explain
why o is equidistant from a b and c
basically you have to prove that this
distance is equal to this distance that
is o a is equal to OB is equal to OC so
this is what you have to basically prove
now the dive in the diagram you see
there are some extrapolated lines so it
which is trying to so show that if you
have a right triangle and if you create
another triangle on the other side these
two triangles together form a rectangle
so this has actually formed a rectangle
now if you recall the properties of
rectangle what do we see we see that in
case of a rectangles the diagonals are
equal in length and also the diagonals
bisect each other now when we see that
diagonals bisect each other that would
mean Oh a will be equal to OC and OB
will be equal to Odin and when we say
the diagonals are equal that means BD
will be equal to AC now considering this
as well as this relation we can very
easily prove that Oh a is equal to OB is
equal to OC that's because when we say B
D is equal to AC what are we actually
saying we are trying to say that BD is
equal to AC so PD is nothing but b au +
OD and AC is nothing but a o + OC right
now since we know that vo is equal to d
bo therefore we can write instead of do
we can write bo similarly here we know
that a o is equal to OC so instead of OC
we can write arrow so from this we can
write
to be both is equal to 200 or we can say
B or is equal to a or so from here we
have proved that Bo is equal to a oh and
from here we saw that a o is equal to
zero therefore we can say that all these
three are equal and therefore o is
equidistant from points a B and C so
with this we have reached towards the
end of this lesson and I hope that this
lesson on quadrilaterals would have
helped you
the most important tip that I would like
to give you in terms of solving
questions related to quadrilaterals is
that focus over on the properties when
you are trying to solve any questions
try to understand the question property
and draw a diagram that should be your
first step when you try to solve a
problem draw a diagram once your diagram
is correct I mean and you remember the
properties I am sure you will be able to
head solve it correctly so with this I
would conclude this lesson so see you
all in the next lesson 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 6 to 12 on physics
chemistry mathematics and biology along
with practical videos so please
subscribe to our channel for daily
updates thank you
quadrilaterals 521 is brought to you by
exam feel calm no more fear from exam
for right angles now when you talk about
quadrilaterals with all sides equal so
all that we can think of the first thing
that comes to our mind is a square where
all sides are equal and all angles are
also equal so basically square would
come here also because in square you
have all right angles so square would
fit into this criteria as well four
sides equal another example would be
rhombus in rhombus also we have four
sides equal but in this case the angles
are not equal now when you talk about
four right angles one two could be
square the other could be rectangle
where all the angles and height angles
but their sides are not equal question
number three name the quadrilaterals
whose diagonals bisect each other now
there are many such quadrilaterals one
such quadrilateral is a parallelogram so
imperil you blame the diagonals bisect
each other you think of the special
parallelograms and they also come under
spiral Oh Graham anyways because all the
tangles are parallelogram all squares
are also parallelogram all rhombuses are
also parallelogram so parallelograms
articles where the diagonals bisect each
other where diagonals are perpendicular
bisectors of each other so this happens
only in case of square and rhombus
diagonals are equal diagonals are equal
this happens again in piece of square
and rectangle so we have proved each of
these properties in detail some time
back so I think you can refer them if
you want to know why this happens
question number four ABC is a
right-angled triangle and O is the
midpoint of the side opposite to the
right angle so right and
this angle that will be so AC is the
side opposite to the right angle explain
why o is equidistant from a b and c
basically you have to prove that this
distance is equal to this distance that
is o a is equal to OB is equal to OC so
this is what you have to basically prove
now the dive in the diagram you see
there are some extrapolated lines so it
which is trying to so show that if you
have a right triangle and if you create
another triangle on the other side these
two triangles together form a rectangle
so this has actually formed a rectangle
now if you recall the properties of
rectangle what do we see we see that in
case of a rectangles the diagonals are
equal in length and also the diagonals
bisect each other now when we see that
diagonals bisect each other that would
mean Oh a will be equal to OC and OB
will be equal to Odin and when we say
the diagonals are equal that means BD
will be equal to AC now considering this
as well as this relation we can very
easily prove that Oh a is equal to OB is
equal to OC that's because when we say B
D is equal to AC what are we actually
saying we are trying to say that BD is
equal to AC so PD is nothing but b au +
OD and AC is nothing but a o + OC right
now since we know that vo is equal to d
bo therefore we can write instead of do
we can write bo similarly here we know
that a o is equal to OC so instead of OC
we can write arrow so from this we can
write
to be both is equal to 200 or we can say
B or is equal to a or so from here we
have proved that Bo is equal to a oh and
from here we saw that a o is equal to
zero therefore we can say that all these
three are equal and therefore o is
equidistant from points a B and C so
with this we have reached towards the
end of this lesson and I hope that this
lesson on quadrilaterals would have
helped you
the most important tip that I would like
to give you in terms of solving
questions related to quadrilaterals is
that focus over on the properties when
you are trying to solve any questions
try to understand the question property
and draw a diagram that should be your
first step when you try to solve a
problem draw a diagram once your diagram
is correct I mean and you remember the
properties I am sure you will be able to
head solve it correctly so with this I
would conclude this lesson so see you
all in the next lesson 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 6 to 12 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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Nov 23, 2024 Last updated |
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