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Byju's Answer
Standard X
Mathematics
Internal Angle Bisector Theorem
ABC and DBC...
Question
△
A
B
C
and
△
D
B
C
are two iosceles triangle on the same base
B
C
and vertices
A
and
D
are on the same sides of
B
C
. If
A
D
is exerted to intersect
B
C
at
P
, show that
△
A
B
P
≅
t
r
i
a
n
g
l
e
A
C
P
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Solution
Given:
△
A
B
C
is isosceles,
A
B
=
A
C
......
(
1
)
Also,
△
D
B
C
is isosceles,
D
B
=
D
C
......
(
2
)
In
△
A
B
C
and
△
D
B
C
, we have
A
B
=
A
C
from
(
1
)
B
D
=
D
C
from
(
2
)
A
D
=
A
D
(common)
△
A
B
D
≅
△
A
C
D
(SSS congruence rule)
So,
∠
B
A
P
=
∠
P
A
C
by CPCT ......
(
1
)
In
△
A
B
P
and
△
A
C
P
,
A
B
=
A
C
(given)
∠
B
A
P
=
∠
P
A
C
from
(
1
)
A
P
=
A
P
(common)
∴
△
A
B
P
≅
△
A
C
P
by SAS congruence rule.
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Similar questions
Q.
△
A
B
C
and
△
D
B
C
are two isosceles triangles on the same base
B
C
and vertices
A
and
D
are on the same side of
B
C
as in figure.If
A
D
is extended to intersect
B
C
at
P
,
Show that
△
A
B
P
≅
△
A
C
P
Q.
Δ
ABC and
Δ
DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that
Δ
ABP
≅
Δ
ACP.
Q.
Question 1 (ii)
Δ
ABC and
Δ
DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that
Δ
A
B
P
≅
Δ
A
C
P
Q.
Question 1 (ii)
Δ
ABC and
Δ
DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that
Δ
A
B
P
≅
Δ
A
C
P
Q.
△
A
B
C
and
△
D
B
C
are two isosceles triangle on the same base
B
C
and vertices
A
and
D
are on the same side of
B
C
(see figure). If
A
D
is extended to intersect
B
C
at
P
show that
A
P
is the perpendicular bisector of
B
C
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