the lines of latitude
All parallels of latitude are parallel to the equator and to each other.
Every line of latitude is parallel to the equator.
parallel
The differences are that the Equator in zero line of latitude. While the Prime Meridian is zero line of longitude. Latitude is horizontal and parallel to the Equator, and longitude runs from pole to pole.
The equator is a parallel because it is a line of latitude that circles the Earth horizontally, dividing it into the Northern and Southern Hemispheres.
The only line that runs parallel through the equator is THE EQUATOR. [The Tropic of Cancer and the Tropic of Capricorn are parallel to the equator, but are north and south of it (respectively) at 23.5 degrees. So they do not run through the equator.] The lines of longitude all run through the equator, but they are not parallel to each other since they all meet up at both the North and South Poles.
parallel
It is the parallel of latitude that runs 66° 33′ 44″ (or 66.5622°) north of the Equator.
The parallels of lattitude
All lines of latitude are parallel with the equator.
There is only one line of latitude on the equator, and the equator is it.
This is the Tropic of Capricorn.