If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps Delta(i)((k) over right arrow) should appear on the different electronic bands i. Here, we introduce intraband Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of Delta(i)((k) over right arrow) in such materials, focusing on lithium iron arsenide (LiFeAs). We identify the three hole-like bands assigned previously as gamma, alpha(2), and alpha(1), and we determine the anisotropy, magnitude, and relative orientations of their Delta(i)((k) over right arrow): These measurements will advance quantitative theoretical analysis of the mechanism of Cooper pairing in iron-based superconductivity.