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Standard VII
Mathematics
Question
If
P
Q
=
P
R
, Show that
P
S
>
P
Q
.
Open in App
Solution
Verified by Toppr
Solution:-
Given : PSR is a triangle.and PQ = PR
To prove:-
P
S
>
P
Q
Proof :
In
△
P
Q
R
,
P
Q
=
P
R
∴
∠
P
Q
R
=
∠
P
R
Q
(
∵
Angles opposite to equal sides are equal
)
Now,
∠
P
Q
R
>
∠
P
S
Q
(
∵
exterior angle of a triangle is always greater than each of its interior angles.
)
⇒
∠
P
R
Q
>
∠
P
S
Q
(
∵
∠
P
Q
R
=
∠
P
R
Q
)
⇒
∠
P
R
S
>
∠
P
S
R
now in
△
P
S
R
,
∠
P
R
S
>
∠
P
S
R
∴
P
S
>
P
R
⇒
P
S
>
P
Q
(
∵
P
Q
=
P
R
)
Hence proved.
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7
Similar Questions
Q1
If
P
Q
=
P
R
, Show that
P
S
>
P
Q
.
View Solution
Q2
In the given figure, if seg PR
≅
seg PQ, show that seg PS > seg PQ.