Question

Q is the mid-point of the side

OR of parallelogram ROSE. A line through R is

drawn parallel to QS meets ES at T and OS produced at P. Prove that RP = 2RT. ​

Answer 1

Answer:

ABCD is a parallelogram 

SL=LR  (L is mid-point)

LQ∥SN

 

In △SRN, L is mid-point of SR and LQ parallel to SN

∴RQ=QN (by mid-point theorem)

SRRL=SNLQ

2RLRL=SNLQ

∴SN=2LQ

∵RQ=QN

RQ=21RN

similarly SP=21RN