There is a lot of missing information here. I can easily devise a scenario where the assertion is false.
Suppose A is 1 cm above L and B is 10 cm above L.
If D and E are on L, clearly CD < CE.
In figure A and B are on the same side of line L. AD perpendicular to l and BE perpendicular to l. If C is the midpoint of AB proove that CD = CE.
2 answers
Ac equal to bc(midpoint)
Draw cm that is median
Triangle cdm is congruent to triangle CME
That is cd epual to ce(cpct)
Draw cm that is median
Triangle cdm is congruent to triangle CME
That is cd epual to ce(cpct)