A line segment can be made up of the addition of different fractions of the line on a straight path i.e a given line segment can be broken into smaller parts.
Therefore, the required proof that EG = HK is shown below:
Given that: EF = JK
FG = HJ
But,
EG = EF + FG .............. 1
and
HK = HJ + JK ............. 2
From equation 1, we have:
EG = EF + FG
= JK + HJ (since EF = JK, and FG = HJ)
So that,
EG = JK + HJ ........... 3
Also from equation 2, we have:
HK = HJ + JK
= FG + EF (since EF = JK, and FG = HJ)
So that,
HK = FG + JK ........... 4
Therefore, comparing equations 1, 2, 3, and 4, it can be concluded that;
EG = HK
For more clarifications on fractions of a line segment, visit: https://brainly.com/question/17374569
#SPJ1
