The Segment Addition Postulate tells us that we can add two segment lengths to get the total length, but only if they share an endpoint.
It is possible for FB>CB but not for AC>BD. See solution.
Practice makes perfect
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.
FB = FC+CB
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.
&FB =FC+CB
&FB > CB
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.
