Question

what allows you to say ac=fh1) distributive property 2) addition property 3) symmetric property 4) substitution property

Answer 1

We know that

$AB=GH,BC=FG$

To prove that AC=FH, we need to use the sum of segments property.

According to the given graph, segment AC is formed by

$AC=AB+BC$

Similarly, FH is defined

$FH=FG+GH$

But, we know by given that AB=GH and BC=FG, that means we can replace this on either equation

$AB=AB+BC\rightarrow AB=GH+FG$

Using the commutative property, we have

$AB=GH+FG=FG+GH$

And we know that FH=FG+GH, so

$AB=FG+GH=FH$

Therefore, AB=FH.