document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #489591 by AlbertusK(3)\"\" \"About 
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It's very simple. You do not need to provide some calculations. \r
\n" ); document.write( "\n" ); document.write( "From your information, we know if angle SPA is 30 and angle PSA is 120.\r
\n" ); document.write( "\n" ); document.write( "from this, we can get angle SAP = 30 and if angle SPA=angle SAP = 30, so triangle
\n" ); document.write( "PSA is a kind of same left-right side, right? (We have AS = PS).--- (1)\r
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\n" ); document.write( "\n" ); document.write( "We also can get angle ARQ = 60 because it has same value with angle SPQ.
\n" ); document.write( "If angle ARQ=60, angle AQR = 60, so the third angle namely QAR is also 60.\r
\n" ); document.write( "\n" ); document.write( "We can conlude if triangle ARQ has the same value for all of it's side. (We have AR=RQ).---(2)\r
\n" ); document.write( "\n" ); document.write( "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).\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "You can sketch this problem for make it more clear.
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