document.write( "Question 1203590: Andaikan ABCD trapesium, E titik tengah kaki AD dan F titik tengah kaki BC. Buktikan bahwa EF=1/2(AB+DC) \n" ); document.write( "

Algebra.Com's Answer #839289 by MathLover1(20849) $\"\"$ $\"About$

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Let $\"+ABCD+\"$ be a trapezium,
\n" ); document.write( " $\"+E+\"$ the midpoint of leg $\"+AD+\"$
\n" ); document.write( " $\"+F+\"$ the midpoint of leg $\"+BC\"$ \r
\n" ); document.write( "\n" ); document.write( "Prove that $\"++EF=%281%2F2%29%28AB%2BDC%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"Capture\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+ABCD\"$ is trapezium in which $\"+AB\"$ || $\"+DC\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"+EF\"$ is parallel to side $\"+DC\"$ . \r
\n" ); document.write( "\n" ); document.write( "Then we have $\"+AB\"$ || $\"+DC\"$ || $\"+EF\"$ .\r
\n" ); document.write( "\n" ); document.write( "Hence we have also trapezium $\"+ABFE\"$ and trapezium $\"+EFCD\"$ .\r
\n" ); document.write( "\n" ); document.write( "Let $\"+AP\"$ be the perpendicular to $\"+DC\"$ and this intersects $\"+EF\"$ at $\"+Q\"$ .
\n" ); document.write( " $\"+AQ\"$ will be perpendicular to $\"+EF\"$ .\r
\n" ); document.write( "\n" ); document.write( "For △ $\"+APD\"$ and △ $\"+AQE+\"$ we have \r
\n" ); document.write( "\n" ); document.write( " $\"+AD%2FEA=+AP%2FAQ=2\"$ \r
\n" ); document.write( "\n" ); document.write( "This gives $\"+AP=2AQ+\"$
\n" ); document.write( "i.e, $\"+AQ=QP\"$ \r
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\n" ); document.write( "\n" ); document.write( "Consider the area we have area $\"+ABCD\"$ = area $\"+ABFE\"$ + area $\"+EFCD+\"$ \r
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\r
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\n" ); document.write( "=> $\"+AP%2A%28AB%2F2%29%2BAP%2A%28+DC%2F2%29\"$
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\n" ); document.write( "\n" ); document.write( " = $\"+AP%2A%28EF%2F2%29+%2BAP%2A+%28EF%2F2%29\"$
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\n" ); document.write( "\n" ); document.write( "= $\"+AP%2A%28%28AB%2BDC%29%2F2%29\"$
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\n" ); document.write( " = $\"+AP%2AEF\"$ \r
\n" ); document.write( "\n" ); document.write( "=>\r
\n" ); document.write( "\n" ); document.write( " $\"+EF=+%28AB%2BDC%29%2F2\"$
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