Question

in the given figure if ts//qr and tv//qs then prove that pv/vs=ps/sr

Answer 1

Given:

In the given figure if ts//qr and tv//qs then prove that pv/vs = ps/sr

To prove:

pv/vs = ps/sr

Solution:

We know that,

If a line is parallel to any one side of a triangle and intersects the other two sides of the triangle, then the line divides the remaining two sides proportionally.

Based on the above theorem, we get:

TS // QR . . . (given)

∴ $\frac{PT}{TQ} = \frac{PS}{SR}$ . . . (1)

and

TV // QS . . . (given)

∴ $\frac{PT}{TQ} = \frac{PV}{VS}$ . . . (2)

Now, on comparing equations (1) and (2), we get

$\frac{PS}{SR} = \frac{PT}{TQ} = \frac{PV}{VS}$

$\implies \frac{PS}{SR} = \frac{PV}{VS}$

$\implies \boxed{\bold{\frac{PV}{VS} = \frac{PS}{SR} }}$

~∎Hence proved∎~

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