We measure spectral features of ~3500 K-selected galaxies at 0.5<z<2.0 from high quality medium-band photometry using a new technique. First, we divide the galaxy sample in 32 subsamples based on the similarities between the full spectral energy distributions (SEDs) of the galaxies. For each of these 32 galaxy types we construct a composite SED by de-redshifting and scaling the observed photometry. This approach increases the signal-to-noise ratio and sampling of galaxy SEDs and allows for model-independent stellar population studies. The composite SEDs are of spectroscopic quality, and facilitate -- for the first time -- Halpha measurement for a large magnitude-limited sample of distant galaxies. The linewidths indicate a photometric redshift uncertainty of dz<0.02x(1+z). The composite SEDs also show the Balmer and 4000 Angstrom breaks, MgII absorption at ~2800 Angstrom, the dust absorption feature at 2175 Angstrom, and blended [OIII]+Hbeta emission. We compare the total equivalent width of Halpha, [NII], and [SII] (W_Halpha+) with the strength of the 4000 Angstrom break (D(4000)) and the best-fit specific star formation rate, and find that all these properties are strongly correlated. This is a reassuring result, as currently most distant stellar population studies are based on just continuum emission. Furthermore, the relation between W_Halpha+ and Dn(4000) provides interesting clues to the SFHs of galaxies, as these features are sensitive to different stellar ages. We find that the correlation between W_Halpha+ and D(4000) at 0.5<z<2.0 is similar to z~0, and that the suppression of star formation in galaxies at z<2 is generally not abrupt, but a gradual process.Comment: Accepted for publication in ApJ; high-resolution version can be downloaded at https://www.cfa.harvard.edu/~mkriek/papers
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