Q. 34.5( 10 Votes )

In figure, if <sp

Answer :

Given: ∆ NSQ ∆MTR


1 = 2


Since,


∆NSQ = ∆MTR


So,


SQ = TR ….(i)


Also,


1 = 2 PT = PS….(ii)


[Since, sides opposite to equal angles are also equal]


From Equation (i) and (ii).


PS/SQ = PT/TR


ST || QR


By converse of basic proportionality theorem, If a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, the other two sides are divided in the same ratio.


1 = PQR


And


2 = PRQ


In ∆PTS and ∆PRQ.


P = P [Common angles]


1 = PQR (proved)


2 = PRQ (proved)


∆PTS - ∆PRQ


[By AAA similarity criteria]


Hence proved.


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