數學,中點/折線定理及證明平行兩個功課問題..(15分)

Q10b.
PD/DB = PQ/QC [proved in (a) part]......(1)
Since ABCD is a parallelogram, so CD//AB
so PD/DB = PR/RT ( intercept theorem).....(2)
From (1) and (2) we get
PQ/QC = PR/RT
therefore QR//CT ( converse of intercept theorem).

2010-04-05 08:54:25 補充：
Q11d.
By mid-point theorem, EG//DC, so triangle EGH is similar to triangle DHC.
therefore EH/HC = 9/18 = 1/2.
But HC = EC - EH = 21 - EH
so EH/(21 - EH) = 1/2
2EH = 21 - EH
3EH = 21
EH = 7.