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ABCD is a parallelogram. The sides AB and AD are produced to E and F

respectively, such that AB=BE and AD=DF.

Prove that: 𝚫BEC≅ 𝚫DCF

Answer:

Solution

"hello students my name is rabbit singh
and i welcome you all to leader learning
homework
one of india's best online classes now
today in this video we have a question
that is based on the topic of
parallelogram
the question says abcd is a
parallelogram the sides a b
and adr produced to e and f now let us
label it as
this is a b c and d
now sides a b a b is produced to e
and this is produced to a d is produced
to f
respectively such that a b this
is equal to b e that means this so
similarly it is showing that b is the
midpoint of a
e and a d is equal to df so d is a
midpoint of af
now we know angle bad is equal to angle
cdf how
angle ba d this angle is equal to angle
c d f how
corresponding angles for parallel lines
if you check
they are corresponding angles of
parallel lines a b and c d
this is a d
this is a b and this is c d these are
parallel lines and also this
parallelogram so
obviously uh opposite sides are parallel
now again if you check
angle bad angle b a d
this angle is equal to angle c b e
again this part same thing corresponding
angles for a b and c d
a b and c d now does angle c d f is
equal to angle c b
this is one now a d is equal to b c
opposite sides of parallelogram
are equal so a d will become equal to b
c
a d is equal to df that is already given
df is equal to
fc now based on that if you check ad is
equal to 80
left hand side equal to bc will become
equal to dm hence
first part proof similarly we will prove
b e is equal to c d b
is equal to b e is equal to
c d this side now in triangle cdf
c d f this triangle
and triangle cpe this triangle
this we have already proved from one
this part
fd is equal to bc from two
here third be is equal to cd from third
so based on that triangles are congruent
to each other how
this is angle this is side and this is
side so based on
sas criterion they are congruent so
triangle b e c
is congruent to triangle dcf so what we
have to prove so we have proved that
science we will write here hence
proved so i think i hope you have
understood the concept very clearly but
still if you have any doubt
do comment in the comment box and please
like and subscribe our channel for lido
thank you"

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