document.write( "Question 1171681: given triangle AKC is isoceles with segment KA is congruent to KC
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document.write( "segment KB bisects angle AKC
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document.write( "prove that angle A is congruent to angle C \n" );
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Algebra.Com's Answer #796590 by ikleyn(52847)![]() ![]() You can put this solution on YOUR website! .\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Compare triangles AKC and CKA (the order of vertices is IMPORTANT (!) ).\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "These triangles have two pairs of congruent sides:\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " the side AK of triangle AKC is congruent to side CK of triangle CKA,\r \n" ); document.write( "\n" ); document.write( " and\r \n" ); document.write( "\n" ); document.write( " the side CK of triangle AKC is congruent to side AK of triangle CKA.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "In addition, these triangles have common angle K between these pairs of sides.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "THEREFORE, according to SAS-test, these triangles are congruent.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Hence, their corresponding angles A and C are congruent.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "At this point, the proof is completed.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |