Class 7 Exam > Class 7 Videos > Mathematics (Maths) Class 7 > Examples: Medians, Altitudes and Exterior angle sum property
Examples: Medians, Altitudes and Exterior angle sum property Video Lecture | Mathematics (Maths) Class 7
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FAQs on Examples: Medians, Altitudes and Exterior angle sum property Video Lecture - Mathematics (Maths) Class 7
| 1. What is a median in geometry? |  |
Ans. In geometry, a median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. Each triangle has three medians, and they intersect at a point called the centroid.
| 2. How is the centroid of a triangle related to its medians? | |
Ans. The centroid of a triangle is the point of intersection of its medians. It divides each median in the ratio 2:1, meaning that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.
| 3. What is an altitude in a triangle? | |
Ans. In a triangle, an altitude is a perpendicular line segment drawn from a vertex to the opposite side or an extension of the opposite side. It can also be referred to as the height of the triangle.
| 4. How is the altitude related to the medians in a triangle? | |
Ans. The altitude and medians of a triangle are different concepts. While the medians connect a vertex to the midpoint of the opposite side, the altitude is perpendicular to a side and intersects the opposite vertex. However, in some special cases, the medians and the altitudes can coincide.
| 5. What is the exterior angle sum property in a triangle? | |
Ans. The exterior angle sum property states that the sum of the measures of the exterior angles of any triangle is always 360 degrees. Each exterior angle of a triangle is equal to the sum of its two remote interior angles.
Text Transcript from Video
hello friends this video on triangle and
its properties part 10 is brought to you
by exam fear calm no more fear from exam
so based on whatever we have studied so
far let us quickly look at some of the
questions question number one in
triangle P Q R D is the midpoint of Q R
that means QD is equal to di right
because D is the midpoint so PM is what
so what does P n so P and then you look
at it PM is basically a line segment
which is drawn from p to its opposite
side such that it is perpendicular on
the opposite side so which is that line
segment which falls perpendicular to the
opposite side that is nothing but
altitudes or height and what is feeding
TDS that line segment which joins the
midpoint of the opposite side to the
vertex so this is nothing but median is
Q M is equal to M R now D is the
midpoint so therefore QD is equal to di
therefore Q M can never be equal to M R
because this part is equal to this part
right so this is this equal no why this
is no that's because M is the point
where the altitude falls on Q R and
altitude doesn't bisect the base it is
always the media which connects to the
midpoint so even if we try to prove this
mathematically we can prove it like this
now since we know that P D is the median
that means D is the midpoint of Q R
therefore Q D is equal to D I so QD can
be written as q m plus m d this is equal
to di right now the question says is Q m
equal to M R so Q M we already have here
but M R we do not have so how can we get
M R so in order to get
we have to add MB to dr so let us do one
thing let us add mb on both sides so
what we do whatever equations it is just
like adding the same value to both side
of the equation so this is our existing
equation and what we do we add mb on
both sides so if we add md on both sides
or do we get we get Q M plus 2 MD is
equal to what is d add plus MD this is
nothing but M R so what do we see we see
that Q M is equal to M R minus 2 MD so
what does this prove this proves that Q
M is not equal to therefore Q M is not
equal to M R so Q M is actually less
than Emma so from M our menu subtract
twines of MD only then you get Q M so
definitely Q M is not equal to M R so
this is how you can even mathematically
prove that the altitude does not bisect
Qi question number to find X so if this
diagram this to triangle two angles of
the triangle is given and we have to
find X now can you tell me what is X
which type of angle is X for this
triangle is it located inside the
triangle no so which are the interior
angles this this and this these are the
interior angles of the triangle so X is
located outside it is located on the
vertex and it is also it also has one
side and one extended side of the
triangle so X is the exterior angle and
while exterior angle property we know
that exterior angle is equal to sum of
opposite interior angle so for X this
would be adjacent interior angle so
these two would be the opposite interior
angles so X will be
one two 65-degree plus forty five-degree
so this is as per the exterior angle
property so 65 plus 45 is 110 degree so
X is equal to 110 degree let's look at
the next one so here also let's see we
have this triangle ABC so again when you
look at X X is an exterior angle because
it is formed outside the triangle and it
has it is formed on the vertex it has
one arm and side of the triangle and the
other arm is extended side so here also
we will make use of the same property so
X will be equal to sum of opposite
interior angles so these are the two
opposite interior angles so X would be
60 degrees plus 30 degrees which is
equal to 90 degrees so the value of x is
90 degrees 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
its properties part 10 is brought to you
by exam fear calm no more fear from exam
so based on whatever we have studied so
far let us quickly look at some of the
questions question number one in
triangle P Q R D is the midpoint of Q R
that means QD is equal to di right
because D is the midpoint so PM is what
so what does P n so P and then you look
at it PM is basically a line segment
which is drawn from p to its opposite
side such that it is perpendicular on
the opposite side so which is that line
segment which falls perpendicular to the
opposite side that is nothing but
altitudes or height and what is feeding
TDS that line segment which joins the
midpoint of the opposite side to the
vertex so this is nothing but median is
Q M is equal to M R now D is the
midpoint so therefore QD is equal to di
therefore Q M can never be equal to M R
because this part is equal to this part
right so this is this equal no why this
is no that's because M is the point
where the altitude falls on Q R and
altitude doesn't bisect the base it is
always the media which connects to the
midpoint so even if we try to prove this
mathematically we can prove it like this
now since we know that P D is the median
that means D is the midpoint of Q R
therefore Q D is equal to D I so QD can
be written as q m plus m d this is equal
to di right now the question says is Q m
equal to M R so Q M we already have here
but M R we do not have so how can we get
M R so in order to get
we have to add MB to dr so let us do one
thing let us add mb on both sides so
what we do whatever equations it is just
like adding the same value to both side
of the equation so this is our existing
equation and what we do we add mb on
both sides so if we add md on both sides
or do we get we get Q M plus 2 MD is
equal to what is d add plus MD this is
nothing but M R so what do we see we see
that Q M is equal to M R minus 2 MD so
what does this prove this proves that Q
M is not equal to therefore Q M is not
equal to M R so Q M is actually less
than Emma so from M our menu subtract
twines of MD only then you get Q M so
definitely Q M is not equal to M R so
this is how you can even mathematically
prove that the altitude does not bisect
Qi question number to find X so if this
diagram this to triangle two angles of
the triangle is given and we have to
find X now can you tell me what is X
which type of angle is X for this
triangle is it located inside the
triangle no so which are the interior
angles this this and this these are the
interior angles of the triangle so X is
located outside it is located on the
vertex and it is also it also has one
side and one extended side of the
triangle so X is the exterior angle and
while exterior angle property we know
that exterior angle is equal to sum of
opposite interior angle so for X this
would be adjacent interior angle so
these two would be the opposite interior
angles so X will be
one two 65-degree plus forty five-degree
so this is as per the exterior angle
property so 65 plus 45 is 110 degree so
X is equal to 110 degree let's look at
the next one so here also let's see we
have this triangle ABC so again when you
look at X X is an exterior angle because
it is formed outside the triangle and it
has it is formed on the vertex it has
one arm and side of the triangle and the
other arm is extended side so here also
we will make use of the same property so
X will be equal to sum of opposite
interior angles so these are the two
opposite interior angles so X would be
60 degrees plus 30 degrees which is
equal to 90 degrees so the value of x is
90 degrees 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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Dec 18, 2024 Last updated |
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