Segment IJ is a midsegment of triangle FGH. IJ = 9, FH = 13, and GH = 16. Find the perimeter of triangle IJH
Since segment IJ is a midsegment of triangle FGH, it means that IJ is parallel to FG and its length is half of the length of FG. Therefore, FG = 2 * IJ = 2 * 9 = 18.
Since FH is a side of triangle FGH, it means that FH is parallel to IJ and has the same length. Therefore, FH = IJ = 9.
Since GH is also a side of triangle FGH, it means that GH is parallel to IJ and has the same length. Therefore, GH = IJ = 9.
The perimeter of triangle IJH is the sum of the lengths of its sides: IJ + JH + IH.
Since IJ = 9, JH = FH = 9.
To find IH, we subtract the length of JH from GH: IH = GH - JH = 16 - 9 = 7.
Therefore, the perimeter of triangle IJH is: IJ + JH + IH = 9 + 9 + 7 = 25. Answer: \boxed{25}.