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State true or false.

In the given figure, $P Q > P R$ and $Q S$ and $R S$ are the bisectors of $∠ Q$ and $∠ R$ respectively. Then $S R > S Q$ .

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True

False

answer is B.

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Detailed Solution

It is given that

P Q > P R

and

Q S

and

R S

are the bisectors of

∠ Q

and

∠ R

respectively.
We have to show that,

S R > S Q

Consider the figure.
The angle opposite the longer side is greater.
Therefore,

P R Q > P Q R

.
Multiply by

12

on both sides,

12 P R Q > 12 P R Q

∠ S R Q > ∠ S Q R

So, the side opposite to

∠ S R Q

is greater than side opposite to

∠ S Q R

.
Therefore,

S Q > S R

.
But the statement is

S R > S Q

.
Hence the statement is false.
Hence the correct statement is for the given triangle PQR, is PQ > PR adn QS and RS are bisectors of

∠ Q, ∠ R

respectively, then SQ > SR.
Therefore option 2 is correct.

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