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Question 14 Exercise 9(A)

Use the information in the given figure to prove:

(i) AB=FE

(ii) BD=CF

Answer:

Solution

"hello students my name is rabbit singh
and i welcome you all to lido 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 congruent
triangles the question says
use the information in the given figure
to prove a b is equal to fe now where is
a b
this is a b is equal to fe and b d is
equal to c
f b d is equal to c f so we have in
triangle abc
you can see this is triangle abc and
triangle efd
e f d a b is parallel to e f it is
already given
so angle abc that means angle a b
c this angle will be equal to angle e f
d
e f d why they are equal they are
alternate angles
so this is the first condition
angles ac is equal to e d that is
already given
you can check
ac in the figure is equal to 80
that is given so that is side so
third angle acb this this angle
is equal to angle this that is also
given that is
third part now based on this if you
check
side angle side angle or aas
congruence criterion triangle abc is
congruent to triangle efd
so based on this we have a b is equal to
fe cpct corresponding part of congruent
triangle
and bc is equal to df vc is equal to df
that's also by
cpct now where is bc this is bc that is
equal to
df this part now but we have to prove
bd is equal to cf this and this so what
we will do
we will add bd plus we will
break bc in two part that will be bd
plus dc
and cf also cf plus dc now after that we
will cancel
dc from both sides and with the
expression that we will be getting is vd
is equal to cf that we have to prove
so 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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