Exercise 37 Page 394

We have two different cases that we need to try. First let's look at $FB>CB$ and then $AC>DB.$

$FB>CB$

Let's try to use the Segment Addition Postulate to prove that $FB>CB$ and see if it works. The postulate tells us that we can add two segment lengths to get the total length of the segments if they are on a straight line.

Since $F,$ $C,$ and $B$ are on a straight line, and in that order, we can express the length of $FB$ with the following equation. Could this help us to prove $FB>CB?$ The $>$ sign means "greater than" and implies that $FB$ has a greater length than $CB.$ From the equation above, we can see that $FC$ and $CB$ add together to be $FB.$ The Segment Addition Postulate can be used to prove that $FB>CB.$

$AC>BD$

We can use the Segment Addition Postulate if we have two segments that share an endpoint. We can then add the segments to get the total length.

The segments $AC$ and $BD$ do not share an endpoint. Therefore, we cannot use the Segment Addition Postulate to prove that $AC>BD.$