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I have two files with identical projections/CRS. Using both OTF on & off I cannot get them to overlap: one shapefile contains coastal polygons of Massachusetts, and the other shapefile contains coastal lines for MA.

 +proj=laea +lat_0=45 +lon_0=-100 +x_0=0 +y_0=0 +a=6370997 +b=6370997 +units=m +no_defs

 +proj=laea +lat_0=45 +lon_0=-100 +x_0=0 +y_0=0 +a=6370997 +b=6370997 +units=m +no_defs 

however the extents are

 xMin,yMin 2321544.64,258328.06 : xMax,yMax 2333464.74,277553.12

vs.

 xMin,yMin -176.685,17.9108 : xMax,yMax -65.2246,71.3413

I've followed the steps in http://qgis.spatialthoughts.com/2012/04/tutorial-working-with-projections-in.html , tried with OTF turned on & off: the layers still do not overlap.

EDIT:

I've saved the MA coast line SHP ( Layer > save as ) using each of the Layer CRS, Project CRS and Selected CRS options: the extent remains the same. As far as I can tell, the chosen projection (EPSG:2163) is a PCS, not a GCS.

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    Although this is framed in ArcGIS for Desktop terms rather than QGIS which you are using, I think the question you are asking is the same as that at gis.stackexchange.com/questions/20572/… – PolyGeo Mar 30 '15 at 22:17
  • There are similar, however I load identical CRSs (and do no reproject), and am looking for a QGIS solution to the extent issue. Maybe I should rephrase the question something like Projection/CRS vs. coordinate system. – user2105469 Mar 30 '15 at 22:27
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    They may both have the same CRS but from the numbers you can see that one is a PCS while the other is a GCS so I would conclude that one has the wrong CRS and it needs to be changed. – PolyGeo Mar 30 '15 at 22:34
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    So this isn't an "extent" adjustment problem, but a projection problem, despite the fact that the meta on both layers indicate the same CRS/PCS. That last bit is what confuses me. In other words, coords. and projections cannot be dissociated. – user2105469 Mar 30 '15 at 22:43
  • Coordinates (they are just numbers) and Coordinate Reference Systems are very loosely coupled by the action of defining their coordinate system ("projection") and requires no projection of coordinate values. – PolyGeo Mar 30 '15 at 23:25
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The coordinates of the second one ares NOT in laea projection, but in degrees.

So you have to Rightclick -> Set CRS for Layer to correct the false CRS information to WGS84 or NAD 83 or NAD27.

I don't know what you did wrong, but you may have done the same error with the first layer as well, and they might still not align after sanitizing only the second layer.

Best way would be to start from scratch with a fresh download of the datasoruces into a new qgis project.

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