SOLUTION: PQRS is a parallelogram and angle SPQ is equal to 60. If the bisectors of angle P and Q meet at A on RS, then prove that A is the mid-point of RS.

Question 813285: PQRS is a parallelogram and angle SPQ is equal to 60. If the bisectors of angle P and Q meet at A on RS, then prove that A is the mid-point of RS.
Answer by AlbertusK(3) (Show Source): You can put this solution on YOUR website!
It's very simple. You do not need to provide some calculations.
From your information, we know if angle SPA is 30 and angle PSA is 120.
from this, we can get angle SAP = 30 and if angle SPA=angle SAP = 30, so triangle
PSA is a kind of same left-right side, right? (We have AS = PS).--- (1)

We also can get angle ARQ = 60 because it has same value with angle SPQ.
If angle ARQ=60, angle AQR = 60, so the third angle namely QAR is also 60.
We can conlude if triangle ARQ has the same value for all of it's side. (We have AR=RQ).---(2)
From ---(1) and ---(2), we know exactly if PS = QR. So from (1) we get AS=PS and from (2) we change QR to PS and we get (AR=PS).
So from this conlusion, we know if AR = AS = PS. Because A is the meet point on RS, it's proved that A is the mid-point of RS.
You can sketch this problem for make it more clear.

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