Question

In the given fig., PS is the median of Triangle PQR, O is any point on PS. QO and RO when produced meet PR and PQ at M and N respectively. PS is produced to T such that OS = ST. Prove that PO : PT = PN : PQ and hence prove that NM ∥ QR

Answer 1

Step-by-step explanation:

first of all construct a triangle give the name pq r

Answer 2

Proved below.

Step-by-step explanation:

Given: PS is the median and QS = SR and OS  = ST

To prove: PO : PT = PN : QN

Proof:

It is given that QS = SR and OS =ST,  

Also S is the midpoint of  OQTR.  

So therefore, OQTR is a parallelogram.

QT║OR and TR║QO

QT║RN and TR║QM

QT║ON and TR║OM  

Now in PQT,

QT║ON

Using Basic Proportionality Theorem,  

PN ║QN = PO║PT

PN : QN = PO : PT                [1]

NM║QR      [from Eq (1)]

Hence proved.