document.write( "Question 1182174: A student tried to trisect an angle G using the following procedure:
\n" ); document.write( "1. Mark off GA congruent to GB.
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\n" ); document.write( "3. Divide AB into 3 congruent parts so that AX=XY=YB.
\n" ); document.write( "4. Draw GX and GY.
\n" ); document.write( "Show that the student did not trisect angle G (Hint: Show that GA>GY. Then use indirect proof to show that angle XGY is not equal to angle XGA.)
\n" ); document.write( "I know how to show that GA>GY (by SAS Inequality) but cannot show why angle XGY is not equal to angle XGA using indirect proof. I appreciate any help! Thanks in advance! \n" ); document.write( "
Algebra.Com's Answer #812170 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I am like you and can see no way that the hint is any good.  But rather than\r\n" );
document.write( "leave you hanging, I'll prove it another way, but also using indirect proof.\r\n" );
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document.write( "△AGB is isosceles GA and GB are congruent\r\n" );
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document.write( "It's easy to prove that △GXY is isosceles.\r\n" );
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document.write( "△GAX and △GBY are congruent by SAS, so GX = GY by CPCT.\r\n" );
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document.write( "Let's assume (for contradiction) that ∠G is trisected and each third\r\n" );
document.write( "of ∠G equals, say k.\r\n" );
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document.write( "Locate point Z such that GZ = GX\r\n" );
document.write( "Draw in XZ\r\n" );
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document.write( "△ZGX ≅ △XGY  by SAS\r\n" );
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document.write( "XZ = XY   by CPCT\r\n" );
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document.write( "XY = AX   given\r\n" );
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document.write( "XZ = AX   transitive axiom (\"things equal to the same thing are equal\")   \r\n" );
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document.write( "△XAZ is isosceles.\r\n" );
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document.write( "∠AZX is acute because base angles of any isosceles triangle are acute.\r\n" );
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document.write( "△GZX is isosceles.\r\n" );
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document.write( "∠GZX is acute because base angles of any isosceles triangle are acute.\r\n" );
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document.write( "∠AZX and ∠GZX are supplementary (they form a linear pair)\r\n" );
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document.write( "We have reached a contradiction because two acute angles cannot be\r\n" );
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document.write( "Therefore the assumption that the student trisected angle G is false,\r\n" );
document.write( "so he or she did not trisect the angle.\r\n" );
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document.write( "Edwin
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