Question 347324: Given XA=ZC Prove AC=ZX
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! I assume by "=" you mean that the two expressions represent the same line segment.
If line segment XA = line segment ZC, then either:
(1) X=Z, A=C, or
(2) X=C, A=Z.
In either case the result follows by substitution. Q.E.D.
If by "=" you mean that two distinct line segments have the same length, then the claim is false. Here's a counterexample:
X=(0,0)
A=(1,1)
C=(2,1)
Z=(3,0)
Then XA = ZC = √2, but
1 = AC ≠ ZX = 3.
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