Question

answer the question plzzz

Answer 1

The construction you have done is correct. The only thing you need to use is 'Converse of Mid-point Theorem' which says,

"Line drawn through the Mid-point of one side parallel to other bisects the third side".

So in triangle RQM,

DN || QM (Construction)

And D is the mid-point of QR (Given)

So from Converse of Mid-point theorem,

N is the mid-point of RM or MN = RN (1)

In triangle PDN,

TM || DN (as QM || DN and TM is a part of QM)

And T is the mid-point of PD (Given)
So From Converse of Mid-point theorem,

M is mid-point of PN or PM = MN (2)


From (1) and (2),

PM=MN=NR

As PM + MN + NR = PR,

3PM=PR

or

PM/PR = 1/3