document.write( "Question 1182026: 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( "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.)\r
\n" ); document.write( "\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 #849999 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "if two sides of one triangle are congruent to two sides of another triangle, then\r\n" );
document.write( "the third side of the triangle with the larger included angle is longer. \r\n" );
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document.write( "GA congruent to GB\r\n" );
document.write( "angle A congruent to angle B\r\n" );
document.write( "AX congruent to YB\r\n" );
document.write( "GX congruent to GY\r\n" );
document.write( "triangle XGY is isosceles\r\n" );
document.write( "GX congruent to GY\r\n" );
document.write( "AX congruent to XY\r\n" );
document.write( "angles GXY and GYX are acute (base angles of an isosceles triangle)\r\n" );
document.write( "angle GXA is obtuse (supplementary to an acute angle)\r\n" );
document.write( "GA > GX   (by the SAS inequality theorem.\r\n" );
document.write( "GA > GY   (since GX is congruent to GY    <-----------STEP M   \r\n" );
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document.write( "For contradiction, assume angle XGY congruent to angle XGA  \r\n" );
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document.write( "Extend GX to twice its length to E such that GX congruent to EX.\r\n" );
document.write( "Draw YE \r\n" );
document.write( "AX congruent to XY (given)\r\n" );
document.write( "GX congruent to EX (by construction)\r\n" );
document.write( "angle GXA congruent to angle EXY  (vertical angles are congruent)\r\n" );
document.write( "triangle GAX and triangle EYX are congruent by SAS\r\n" );
document.write( "GA congruent to EY  (c.p.c.t)      <----------------- STEP N \r\n" );
document.write( "angle XGA congruent to angle YEX (c.p.c.t.)\r\n" );
document.write( "angle YEX congruent to angle XGY\r\n" );
document.write( "Triangle GYE is isosceles  (base angles congruent)\r\n" );
document.write( "GY congruent to EY  (c.p.c.t)     <------------------ STEP P\r\n" );
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document.write( "From steps N and P above,\r\n" );
document.write( "GA is congruent to GY              <----------------- Step Q\r\n" );
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document.write( "Step Q contradicts Step M.\r\n" );
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document.write( "Therefore, the assumption that angle XGY congruent to angle XGA\r\n" );
document.write( "is false, so the student did not trisect angle AGB. \r\n" );
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document.write( "Edwin
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