Fresnel's equations: relation between powers and reflectance and transmittance of the parallel and perpendicular components

According to Hecht’s Optics book, the reflectance, $R$, and the transmittance, $T$, are defined as the ratios of the incident power and the reflected and the transmitted powers, respectively:

$$R equiv frac{I_{r}}{I_{i}}, quad T equiv frac{I_{t} cos theta_{t}}{I_{i} cos theta_{i}}$$

Then, if $R_perp$, $R_parallel$, $T_perp$ and $T_parallel$ are the reflectances and transmittances of the components of light perpendicular and parallel to the plane-of-incidence, would this be true?

$$R_parallel = left(frac{I_{r}}{I_{i}}right)_parallel quad(1) quadquadquad T_parallel = frac{ cos theta_{t}}{ cos theta_{i}}left(frac{I_{t}}{I_{i}}right)_parallelquad(2)$$

$$R_perp = left(frac{I_{r}}{I_{i}}right)_perp quad(3) quadquadquad T_perp = frac{ cos theta_{t}}{ cos theta_{i}}left(frac{I_{t}}{I_{i}}right)_perp quad(4)$$