![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
you are given that XZ < YZ.
\n" ); document.write( "you want to prove that angle X is not equal to angle Y.
\n" ); document.write( "draw your triangle so that angle X is on the left and angle Y is on the right and angle Z is on top.
\n" ); document.write( "assume that angle X is congruent to angle Y.
\n" ); document.write( "drop a perpendicular from angle Z to intersect with XY at A.
\n" ); document.write( "you will get:
\n" ); document.write( "angle X is congruent to angle Y (assumption).
\n" ); document.write( "ZA is congruent to ZA (reflexive property).
\n" ); document.write( "angle XAZ and angle YAZ are right angles (perpendicular lines form right angles).
\n" ); document.write( "angle XAZ is congruent to angle YAZ (right angles are congruent).
\n" ); document.write( "triangle XAZ is congruent to triangle YAZ (AAS).
\n" ); document.write( "XZ is congruent to YZ (congruent parts of congruent triangles are congruent to each other).
\n" ); document.write( "this is a contradition since you were given that XZ is not equal to YZ, so the assumption that angle X is congruent to angle Y is invalid.
\n" ); document.write( "this proves that angle X is not congruent to angle Y by contradiction.
\n" ); document.write( "therefore angle X is not equal to angle Y (end of proof).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "