Question

In the given figure, PS = 3RS. M is the midpoint of QR. If TR || MN || QP, then prove that:

RT = `(1)/(3)"PQ"`

Answer 1

Proof:
R and T are the mid-points of NS and MS respectively.

⇒ RT = `(1)/(2)"MN"`

M and N are the mid-points of  LT and PR respectively.

⇒ MN = `(1)/(2)"PQ"`

So, RT = `(1)/(2)(1/2 "PQ")`

⇒ RT = `(1)/(4)"PQ"`.