F.3 MAHTS~急

http://i41.photobucket.com/albums/e278/hkwod/SNC13257.jpg:
ABCD is parallelogram,
so AB = CD, AD = BC, angle SAP = angle QCR, angle SDR = angle PBQ

Because AP = RC, so DR = BP. Simiarly, AS = CQ.
Therefore, Triangle SAP = Triangle QCR (SAS) & Triangle PBQ = Triangle RDS (SAS)**

Then SP = RQ, SR = PQ (Because of **)
So, PARS is parallelogram

http://i144.photobucket.com/albums/r199/hei156/MATHS/DSCN0527.jpg:
tan angle ABC = 8/6
Angle ABC = 53.130

sin angle ABC = AD/6
AD = 4.8

cos angle ABC = BD/6
BD = 3.6

angle ACB = 180 - 90 - 53.130
angle ACB = 36.8699

cos angle ACB = CD/8
CD = 6.4

http://i144.photobucket.com/albums/r199/hei156/MATHS/DSCN0526.jpg:
Triangle DEF ~ Triangle ACF (AAA)
So, DE/AC = DF/AF
10/AC = 10/30
AC = 30

Triangle ABG ~ Triange DEG (AAA)
So, DG/AG = DE/AB
DG/AG = 12/12
DG = AG
DG = 20

http://i144.photobucket.com/albums/r199/hei156/MATHS/DSCN0525.jpg:
Triangle ABC ~ Triangle ADE (AAA)
So, h/(h+15) = 12/18
h = 2/3h + 10
h = 30
& k/(k+21) = 12/18
k = 2/3k + 14
k = 42

Triangle BCE ~ Triangle FAE (AAA)
so, j/33 = 21/42
j = 16.5
& i/18 = 42/21
i = 36

http://i41.photobucket.com/albums/e278/hkwod/SNC13257.jpg