Question

In the given figure, if TS || QR and TV || QS, then prove pv/vs=ps/sr​

Answer 1

Answer:

wkt, TS||QR

then, PT/TQ= PS/SR. ( BPT) --1

lly, TV|| QS

then, PT/ TR= PV/VS( BPT)---2

From equation 1 and 2

PS/SR= PV/VS. ( AXIOM 1)

Therefore,

PV/ VS= PS/SR

Hence proved

Answer 2

PV/VS=PS/QS.

Given,

In the given triangle, TS is parallel to QR and TV is parallel to QS.

To prove,

The ratio of PV and VS is equal to the ratio of PS and QS.

Solution,

We have a triangle PQR.

In the Triangle, T and S divide PQ and PR in the same ratios respectively.

Also, in the small triangle PQS, T, and V divide PQ and PS in the same ratios respectively.

As In ∆PQR

TS || QR

So, By Basic Proportionality theorem

The BPT states that if a line is drawn parallel to one side in a triangle, then the line divides the remaining two sides in the same ratio.

PT/TQ=PS/SR.....equation 2.

Similarly, In ∆ PQS

TV || QS

PT/TQ=PV/VS.....equation 1

From Equations 1 and 2.

PV/VS=PS/QS

Hence Proved.

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