A relatively simple and efficient high-frequency analysis of electromagnetic modal reflection and transmission coefficients for waveguide discontinuities which are formed by joining different waveguide sections is presented. The analysis extends the concept of geometrical theory of diffraction based equivalent edge currents and utilizes it in conjunction with the reciprocity theorem to describe interior (waveguide) scattering effects. It is noted that the previous use of equivalent edge currents was mostly restricted to exterior scattering by edged bodies, and its application to deal with interior scattering was limited to those guide geometries for which image theory could be used effectively to account for the interior wall effects. The present extension allows one to treat more general two- and three-dimensional waveguide geometries provided the waveguide modes and their associated modal rays can be found explicitly. In particular, expressions for two-dimensional reflection and transmission coefficients are developed, and numerical results are shown for a flanged, semi-infinite parallel plate waveguide and for the junction between two linearly tapered waveguides. One sample result is also shown for the reflection coefficient of a three-dimensional open-ended circular waveguide. Detailed expressions for three-dimensional waveguide discontinuities are being reported separately.