Exercise 19 Page 16

To find $FH,$ we should use the Segment Addition Postulate. This postulate tells us that, if we have a point between two points, we can add the lengths of the two smaller segments to find the longer segment length. In our case, $H$ is between $F$ and $G,$ so $FG$ is the sum of $FH$ and $HG.$ From the diagram, we know that the length $FG$ is $37$ and the length $HG$ is $13.$ Now, we can use this to calculate $FH.$ The length $FH$ is $24.$