p is a point on the bisector of angle abc if the line through p parallel to ba meet BC at Q prove that bpq is an isosceles triangle
Answers
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Answer:
To prove: BPQ is an isosceles triangle.
According to the question,
Since, BP is the bisector of ∠ABC,
∠1 = ∠2 … (1)
Now, PQ is parallel to BA and BP cuts them
∠1 = ∠3 [Alternate angles] … (2)
From equations, (1) and (2),
We get
∠2 = ∠3
In Δ BPQ,
We have
∠2 = ∠3
PQ = BQ
Hence, BPQ is an isosceles triangle.
Step-by-step explanation:
To prove: BPQ is an isosceles triangle.
According to the question,
Since, BP is the bisector of ∠ABC,
∠1 = ∠2 … (1)
Now, PQ is parallel to BA and BP cuts them
∠1 = ∠3 [Alternate angles] … (2)
From equations, (1) and (2),
We get
∠2 = ∠3
In Δ BPQ,
We have
∠2 = ∠3
PQ = BQ
Hence, BPQ is an isosceles triangle.
n : In
Δ
A
B
C
,
P
is a point on the bisector of
∠
B
a
n
d
f
r
o
m
,
P
,
R
P
Q
|
|
A
B
is drawn which meets BC in Q
To prove :
Δ
B
P
Q
is an isosceles
Proof :
∵
BD is the bisectors of CB
∴
∠
1
=
∠
2
∵
R
P
Q
|
|
A
B
∴
∠
1
=
∠
3
(
(
Alternate angles)
But
∠
1
=
∠
2
(
P
r
o
v
e
d
)
∴
∠
2
=
∠
3
∴
P
Q
=
B
Q
(Sides opposite to equal angles)
∴
Δ
B
P
Q
is an isosceles
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