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- Chapter 7- Indices [exponents]
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- Chapter 24- Solution Of Right Triangles
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Question 1 Exercise 9(A)

Which of the following pairs of triangles are congruent? In each case, state the

condition of congruency:

(a) In 𝚫 ABC and 𝚫 DEF, AB=DE, BC=EF and ∠B=∠E.

(b) In 𝚫 ABC and 𝚫 DEF, ∠B=∠E = 90° ; AC=DF and BC=EF.

(c) In 𝚫 ABC and 𝚫 QRP, AB=QR, ∠B=∠R and ∠C=∠P.

(d) In 𝚫 ABC and 𝚫 PQR, AB=PQ, AC=PR, and BC=QR.

(e) In 𝚫 ABC and 𝚫 PQR, BC=QR, ∠A=90°, ∠C=∠R=40o and ∠Q=50°.

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 basically we have five
questions parts in which we have to tell
which criteria will be following
in order to prove the two triangles
congruent now which of the following
pairs of triangles are congruent
in each case state the conditions of
congruency now
first part in triangle abc and triangle
d e f a b is equal to d that means side
bc is equal to e f that means side
and angle b central angle will be equal
to angle e
so triangle abc
will be congruent to triangle def
by side angle side criterion that is
sas criterion similarly for the second
one
in triangle abc and triangle def angle b
and angle e are 90 degree
that means angle ac
is equal to df so that means side and bc
is equal to ef that means again side so
this criterion is also
sas triangle abc and triangle def are
congruent based on ss criterion
third in triangle abc and triangle qrp
a b is equal to qr that is side angle b
is equal to angle r that is angle
and angle c is equal to angle p so that
is again angle
so based on aas criterion triangle abc
is congruent to triangle qrp
now second last in triangle abc and
triangle pq are
a b is equal to pq that means first side
ac is equal to pr that means second side
and bc is equal to qr that means third
side so all the three sides
that means triple s criterion triangle
abc
is congruent to triangle pqr last
in triangle abc and triangle pqr bc is
equal to qr
first side angle a is equal
to 90 degree
and angle q is equal to 50 degree
so an angle c and r are 40 degree so
first side are equal
and second angle are equal and
angle a is 90
and angle c and angle are okay so let us
make the figure for this question
this is triangle abc
in which angle a sorry this is a this is
b
and this is c because angle a is given
90 degree
so angle a is 90 degree similarly
in the second figure angle q is given an
angle r is given
so angle q is
50 degrees so this is q
that is 50 degrees p is 90 degrees
and pqr
r is given 40 degrees
now if we check based on this a is 50
is 90 b is 90
so that is given angle c is equal to
angular 40 degrees that is already given
angle c is equal to angular 40 degrees
that is already given an angle q and
angle b
are 50 degrees so based on aas criterion
triangle abc is congruent to triangle
pqr
based on this figure 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 follow
thank you"

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