collinear points gk=45, hl=18, and gh=hi=i. find the length of each segment

To find the length of each segment, we need to determine the values of gk, hl, gh, hi, and i. From the information given, we know that gk = 45 and hl = 18. Now, let's break down the other unknown lengths step by step.

First, let's look at the segments gh, hi, and i. Since they are all equal in length, we can assign a variable, let's say "x", to represent the length of each segment. Therefore, we have gh = hi = i = x.

Now, let's consider the two given segments, gk and hl. Since the points gk and hl are collinear with the points gh, hi, and i, we can add their lengths to find the total length of the line. In other words, gk + gh + hi + hl = gk + x + x + hl.

Substituting the given values, we have:

45 + x + x + 18 = 45 + 2x + 18.

Simplifying the equation:

45 + 2x + 18 = 45 + 2x + 18,
63 + 2x = 63 + 2x.

Since the equation is identity, the value of "x" can be any real number. Therefore, we cannot determine the exact value of gh, hi, and i without further information.

In conclusion, the length of each segment gh, hi, and i cannot be determined based on the given information.