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I'm asked to work on some road shapefiles and create a map out of it. The problem is that some of the shapefiles doesn't have a coordinate reference system which then I noticed that they don't have .prj files.

I tried defining their projection (WGS 84, same as the other shapefiles) using Define Shapefile Projection tool in QGIS which created .prj files for them but when I put a base map, they're in the middle of the sea. I even tried Define Projection in ArcMap but it has the same result

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If the roads are local to where you live, then they are possibly in a local projected coordinate system.

For example, I live in Perth, Australia. If i had the same problem, I would have done the same, checked it for Geographic Project first (ie: WGS84, or GDA94).

Failing that, Perth would really only ever use two other coordinate systems. MGAz50 or PCG.

These are local coord systems.

So depending upon where you live and the extent of the data, seeing as though you seem to have eliminated them being a Geographic Coord System, try applying a projected coord system.

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    What @nr_aus said. This is a bit of trial and error, try to find out what are the usual local coordinate systems for the actual area (e.g. if the data are from Europe, it is possibly some UTM zone if it is not covering a too large area) In QGIS the quickes way of doing this is to use Layer Properties - Settings and set a new assigned coordinate system. Aug 13, 2021 at 6:55
  • I tried to use WGS 1984 UTM Zone 51N which should be in the northern hemisphere and around the longitude of the Philippines but it still ends up in the middle of the pacific ocean in the southern hemisphere
    – Leptres
    Aug 13, 2021 at 9:52
  • try a bunch of Philippines here epsg.io/?q=Philippines
    – nr_aus
    Aug 13, 2021 at 10:23
  • It might help if you tell us the expected place on Earth and the extent of the shapefile, as reported by the layer properties - General Information tab after loading it into qgis. If it is less than 180/90, geographic CRS are recommended, otherwise projected CRS.
    – AndreJ
    Aug 14, 2021 at 10:24

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