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Help! can not perform overlay!

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Hello-

This is my first time to perform "overlay", I guess the problem has something to do with geographical coordinates.

Basically, I am trying to overlay two layers, in order to redistrict the map and obtain information by the new boundaries, but nothing comes out of the function "union" (I keep getting one same unchanged input layer).

Then, I checked the coordinate systems of the two input layers. Layer A is "GCS_North_American_1983" and not projected. Layer B is "GCS_North_American_1983" and projected with "NAD_1983_Lambert_Conformal_Conic".

When I add them to the same data frame, they appear to overlap (both are the State of Texas, layer A is by counties, layer B is by congressional districts), but nothing comes out of the "Union" function. My guess is that although they appear to overlap, but they don't actually.

Then I used the projection tool, and changed their coordinate systems, so that both of A and B are "GCS_North_American_1983", unprojected. Then A and B don't appear to match anymore, one is floating away from another.

The above is all the information I can provide, with my limited knowledge about GIS (Especially about projection), I couldn't figure out what part went wrong.

I have been struggling with it all day, please help!

Thank you! guys!

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