How to get correct lengths when switching from GCS to PCS?

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I'm working on ArcMap 10 and need to get the lenghts (in meters) of the segments composing my line feature class. CGS of the line is WGS_1984. I thought the correct way was to switch the Data Frame to PCS: WGS_1984_World_Mercator in order to get metric lengths with Calculate Geometry in a newly added field. I guess I was wrong since as I use the ruler to check if lengths are correct I see they are not (When I used the ruler with Data Frame set on GCS the lenghts were correct).Am I doing it wrong or it is impossible to get the same lenghts with GCS and PCS?



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