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Byju's Answer
Standard IX
Mathematics
RHS Criteria for Congruency
In the alongs...
Question
In the alongside diagram, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B.
State whether true or false for the following equation
PQ = CD
A
True
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B
False
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Solution
The correct option is
A
True
Let
O
be the point of intersection of the angular bisectors
A
P
,
a
n
d
Q
B
We know that,
1) Angular bisectors intersect at
90
∘
.
2) Angular bisectors bisect each other, i.e.,
A
O
=
O
P
and
B
O
=
O
Q
Join QP, to form
△
P
O
Q
Consider
△
A
O
B
and
△
P
O
Q
,
A
O
=
O
P
∠
A
O
B
=
∠
P
O
Q
=
90
∘
B
O
=
O
Q
The two triangles are congruent. Hence the side
A
B
and
Q
P
must be equal. Hence, parallel.
We know that, in parallelogram
A
B
C
D
,
A
B
=
C
D
and
A
B
∥
C
D
Hence,
C
D
=
Q
P
and
C
D
∥
Q
P
. Proved.
Suggest Corrections
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