We know that
[tex]AB=GH,BC=FG[/tex]
To prove that AC=FH, we need to use the sum of segments property.
According to the given graph, segment AC is formed by
[tex]AC=AB+BC[/tex]
Similarly, FH is defined
[tex]FH=FG+GH[/tex]
But, we know by given that AB=GH and BC=FG, that means we can replace this on either equation
[tex]AB=AB+BC\rightarrow AB=GH+FG[/tex]
Using the commutative property, we have
[tex]AB=GH+FG=FG+GH[/tex]
And we know that FH=FG+GH, so
[tex]AB=FG+GH=FH[/tex]
Therefore, AB=FH.
