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When I opened in QGIS the shapefile of Berlin, which I downloaded from the Berlin government website, the shape of map is flattened. I wonder how I can make this flattened map right?

I attached the image of flattened map in ArcMap and the right map of Berlin to compare.

enter image description here

enter image description here

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The project CRS is in a projection that looks flattened. Change the project CRS to another CRS like EPSG:3857 or the local UTM-zone - the last option is better in your case, as you have only a small area on your map).

For Berlin, use DE_ETRS89 / UTM CRS, EPSG:25833, see: http://crs.bkg.bund.de/crseu/crs/eu-description.php?crs_id=Y0RFX0VUUlM4OSAvIFVUTQ==

To change project CRS in QGIS, click on the button on the bottom right. Do not set (change) the layer CRS, see here for details: https://gis.stackexchange.com/a/383437/88814

I guess the project is set to a geographic CRS (EPSG:4326) because the layer is saved in this CRS (as can be seen on your screenshot). At least QGIS sets the project CRS by default to the same CRS as the first layer you load. Probably something comparable happened in your ArcMap. Once again: Don't touch the layer, it can stay in this CRS, but change the project CRS.

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