Basic Proportional Theorem Video Lecture - Class 9

Harris friend I am ashish Avila in the
last class we discussed about the basic
proportionality theorem and the converse
of basic proposition theorem in this
class we discussed the problem based on
basic proportionally theorem and it's
converse so let's start with the problem
the first problem
or in this given figure de is parallel
to BC and we have to find the length of
AE as well as ec oh so they came casa
find carrying it oh Jessica me pathetic
aqui de is parallel to BC this is my
basic property terminal gossip in some
bowling you're going according to bpt a
DD upon DB is equal to AE upon ec that
is why BPD
by bpt we can say that okay Oh a dma by
that is 3d BMI betha that is five or a
or e see how many paths on so let's say
Chucky a ce qu'il n24 the Ricky let's m
is equal to the a X a third 24 Messier
part access to batch of apart Kip Naga
24 minus X ok so i'll put the values 80
degrees yoga 3 DB each other five a ki
jagah x ECG yoga 24 minus x ok cross
multiplying it tho 3 into 24 minus x is
equals 25 I now three into 24 that is 72
minus 3x equals 25 X so 72 equals 28 x
so x equals 2 72 x 8 that is 9 so the x
is nine though that is a so you can keep
me away x that is nine or ec that is 24
minus X that is 24-9 that is 15 so this
there is a home sites but also thing by
using the basic property theorem now
next question
and this given figure de is parallel to
BC llame given it or you be given a key
Fe joha it is parallel to DC we have to
prove prove that proved that ad square
is equals to a B into a f.a.b into AF
EMA proof corner to the chicas are
preferring a parish is the Yankee jaja
p.m. a parallel lines measure a theme to
hop it was triangles key on the rom bpt
velocity just a key immature de or VC
parallels Eric here so in triangle ABC
de is parallel to BC to buy bpt we can
say that ad upon ad upon ad upon a B is
equals to a upon ec a upon AC so this is
bye bpt okay Abby PTAB results tomorrow
the basic result the ad upon davita
making um ad upon a BB voice acted given
f of last class in watauga that is ad up
on a beach is equal to AE upon a C so
this is bobby BTW we can say that now
okay all consider in federal major
argument i feel neither are you d ck
paddle so in triangle ADC in triangle
ADC fe is parallel to DC to buy BBT we
can say that AF upon ed is equals to a
upon AC again by BBT we can say that so
this is equation number one let's see
and this is equation number two now as
we compare first and second as we
compare first and second we can say that
their right hand sides are equal so the
left-hand sides are also equal so ad
upon a B is equals to a f of 180 Abscam
cross multiply cutting it so a d square
18 to 80 get naga 80 square is equals a
FN to AV took a my proof another so this
is our result so it's Kobe mhmm by use
of bpt may prove cardium now the next
question
show that centroid divide show that
centroid divide median in the ratio to
is 210 make a show gonna eat triangle
cazzo centered with a medium could lose
2-1 gear ratio my divided further
central java median intersection
let's say we have a triangle ABC let's
say yuck i'm a comedian Rokia ad
mediately the equal parts may divide
Krieger let's ni equal median drop here
lets it be e CB du equal parts might
vital Jenga or EMR a centroid oh yeah
that is in G ok go huh my blue corner we
have to prove here AG is to GD is to is
to 1pm approve Cardinal so let's see the
proof ok the proof token is a polemic
which construction kearney breaking you
have to do first construction the
pallium construction carrying
construction a mahogany we have to
produce ad to the point to the point
edge such that B H is equals to GD ok
this key jolanta will be a DHD jolanta
GDK wherever you guys there's some
produce screen now finally join bh and
HC join bh and HC now let's see the
proof
so agar hum quadrilateral ve we have to
join GC also now the party lateral be at
c g go Graham they came to me they
cranky is quadrille it'll be at cgk your
diagonal say whoppers make this will go
by set current diagonal bisect
each other or Amazon thankee over QC
quadratic a diagonal bisect array so
quadrilateral be hCG is parallelogram
this comparative rumbles a thing again
this is sufficient condition for a
quadrilateral to become a parallelogram
agar kisi quadrilateral key diagnose a
QC Co beset correcto some padded ohh
grumbles of thing so it is a pentagram
throw a parallelogram hair the Humboldt
suck thank you Joe 9bg head it is
parallel to Etsy or or BG Co ok produced
connect image-line GEB Maria from who he
was thinking so G is also parallel to HC
g is parallel to at sea now aigerim
triangle a HC cody came in triangle aah
SI GE is parallel to HC so by bpt we can
say that AG upon GH AG upon GH is equal
to AE upon ec e upon pc or animal omega
midpoint on the AE or ECE college is so
they are canceled each other we are
getting one so AG is equal to G H then
AG or GH we're averaging it AG is equals
to G or GH combos event price of GD is
figure go they trembles at then he ate
ghg Ohio twice of GD h john d is the
midpoint of GH so GD OG h ere it is
twice of GD the NEM ghd jagged choice of
Gd licks of thing twice on GD so GD go
another shift here so 80 x GD x equal to
x 1 or you can say that EG is to GD is
to is to one document proof can anthem
so this is the proof that the centroid
divides the median in the ratio 2 is to
1 now the next question
prove that the diagonal of a trapezium
divides each other proportionally
I make a Shogun a key trapezium killer
diagonal so they make this rico same
ratio may intersect car thing let's say
we have a trapezium
is the diagonals
a b c d oh how many prove karna we have
to prove that diagonals divides each
other proportionally that is OD upon OB
is equals to 0 °c upon OA EMF row corner
now in order to prove this vo to do one
construction draw a line from a parallel
to AV draw OG parallel to AV as well as
parallel to CD if your CD already
paralleling can get rejected easier now
we consider a triangle proof let's see
the proof in triangle a 0 d triangle aod
go taking it or chuck e 0 g is
perpendicular to DC oh geez
perpendicular to DC so Islam vpt laga
cables at their key AG upon GD is equals
to pay a point or see you Bozek that is
by BBD orascom reciprocal car here
licking some breaks at then GD upon AG
is equals to OC by boy let's say this is
your equation number 1 now permit
triangle d a BK fo triangle d a B code a
cane or a smell monument OG is parallel
to a B this mega pop is MVP Tila kind by
basic proportionately theorem from ball
sack then DG by GA or GD by AG is equals
to OD x 0 be 0 dy 0 b that is equation
number 2 now first row second program
compare cousin ki left hand side equal
it by comparison first into their left
hand sides are equal so their right hand
side sorry also equal that is OC x 0 a
4c by a is equals to 0 d by movie that
is by comparison so this is our result
then a trapezium a diagnostic Lucy Koh
same ratio may God something so Kaiba
reproof bachata Kaiba couch numerical
values Jacobs a couch unknown fine
technically
that this result come directly use
curseth name now let's see the next
result also if a line is drawn parallel
to one side
of trapezium
then it will divide the non-parallel
side
in the same ratio
question key question here you may pasok
trapezium
trapezium ABCD or avarom a client Drogo
range which is parallel to the parallel
side of the museum AV or CD parallel
sites a twinkie perelman decline in
brokering that say this is EF you have a
given a levy parallel to CD added to the
f we give an MA so I'm a pro kappa nike
agent Linehan whoa non-parallel site
that is ad or c v co same ratio may
divide caregiver club de upon EA this
equals to C F up on FB what we have to
prove that is EE upon EA is equal to CF
up on FB the school curriculum a
construction kurung it I'm gathering a
DB for joy incurring gay let's say D
beam intersects is called jeepers join
DV intersect EF at g ok now let's see
the proof of it
in triangle bab EG is parallel to a be
so by BPD we can say that de upon EA is
equal to DG upon gb that say this is our
equation number one now in triangle BCD
FG is parallel to CD now by VPD we can
say that we can say that bf upon FC BF
upon FC is equals to G be upon DG OS
kokomi reciprocal girl Kelly Kuhn
thermal exit from FG upon V F is equal
to DG upon gb let's say this is equation
number two now again I'm first row
second you compare current 20 right hand
side equal it the left hand side also
ecology so compare one and two we can
say that de upon EA is equals to F G
upon beer so this is our result that a
line drawn parallel to the parallel side
of a trapezium divides the non-parallel
sites in the same ratio thank you