Many amateurs think that the half wave dipole antenna has a 50 ohm feed point impedance!
“A true half-wave dipole is one half of the wavelength λ in length, where λ=c/f in free space. Such a dipole has a feedpoint impedance consisting of 73Ω resistance and +43Ω reactance, thus presenting a slightly inductive reactance. In order to cancel that reactance, and present a pure resistance to the feedline, the element is shortened by the factor k for a net length l of: l 1/2 kλ = 1/2 k c/f ”
So we can see the reactance is cancelled by shortening the antenna by a small amount, however the feed point resistance will still be above the hallowed 50 ohms resistance desired by many amateurs. A common method used to achieve a good match to 50 ohms is to drop the ends of the dipole to form an inverted V of approx 45 degrees. It is very difficult to obtain a low SWR on a purely horizontal half wave dipole fed with 50 ohm coax: if you dont believe me give it a try.