[en] An inhomogeneous deflecting magnet and slotted disk velocity analyzer combination has been used to deflect aside nonreactively scattered Li atoms and thereby measure velocity distributions of LiBr and LiCl reactively scattered from crossed thermal beams of Li and Br₂ or Cl₂. Transformation of these data into the center-of-mass coordinate system provides contour maps of the differential reactive cross sections which indicate that the Li+Br₂ and the Li+Cl₂ reactions have the following features in common: (a) The reaction mechanisms are direct; (b) The product angular distributions are broad although foward scattering is preferred (i.e., LiX scattered in the direction of the Li velocity); (c) Small product recoil energies are most probable but the product recoil energy distributions have a long tail. There is a strong coupling of the product recoil angle and energy distributions for Li+Cl₂→LiCl+Cl with forward scattering favoring higher product recoil energy; however, this coupling phenomenon is weak or nonexistent for the Li+Br₂→LiBr+Br reaction. Semiquantitative observations are also presented for the Li+ICl reaction. These results are discussed in relation to previous experimental and theoretical work on the reactions of alkali atoms with halogen molecules