Answer to Question #94834 in Geometry for Fuseini Suhuyini Firdaus

Question

In a parallogram ABCD, P divides AB in the ratio 2 : 5 and Q divides DC in the ratio 3 : 2. If AC and PQ intersect at R, find the ratios AR : RC and PR : RQ.

Answer 1

AP:PB = 2/5
DQ:QC = 3/2

AR/RC - ?
PR/RQ - ?

show triangels APR and QCR
angle PAR = angle RCQ (AB || DC)
angle ARP = angle CRQ
tnen angle APR = angle RQC and triangle APR ~ trtiangle QCR
AP = 2/7 * AB
PB = 5/7 * AB
DQ = 3/5 * DC
QC = 2/5 * DC
AB = DC
2/7 = 2*5/7*5 = 10/35
5/7 = 25/35
3/5 = 3*7/5*7 = 21/35
2/5 = 14/35
AP = 10/35 * AB
PB = 25/35 * AB
DQ = 21/35 * AB (AB=DC)
QC = 14/35 * AB
suppose that AB/35 = x
then 
AP = 10x
PB = 25x
DQ = 21x
QC = 14x
if triangle APR ~ triangle CQR then
PR/RQ = AR/RC = AP/CQ = 10x/14x = 10/14 = 5/7