SOLUTION: Please help me solve this proof! Given: XZ < YZ Prove: angle X is not equal to angle Y Thank you :)

Question 934317: Please help me solve this proof!
Given: XZ < YZ
Prove: angle X is not equal to angle Y
Thank you :)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you are given that XZ < YZ.
you want to prove that angle X is not equal to angle Y.
draw your triangle so that angle X is on the left and angle Y is on the right and angle Z is on top.
assume that angle X is congruent to angle Y.
drop a perpendicular from angle Z to intersect with XY at A.
you will get:
angle X is congruent to angle Y (assumption).
ZA is congruent to ZA (reflexive property).
angle XAZ and angle YAZ are right angles (perpendicular lines form right angles).
angle XAZ is congruent to angle YAZ (right angles are congruent).
triangle XAZ is congruent to triangle YAZ (AAS).
XZ is congruent to YZ (congruent parts of congruent triangles are congruent to each other).
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.
this proves that angle X is not congruent to angle Y by contradiction.
therefore angle X is not equal to angle Y (end of proof).

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