Yes. That's a big part of the reason why the lines are often called "parallels".
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Lines of latitude.
Lines of latitude are horizontal and run parallel to the poles
Parallels are lines that run the same direction and are the always the same distance apart. On a map (and the Earth) the lines of latitude (measurement North and South of the equator) are parallel.
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.
The term that indicates imaginary parallel lines that circle the Earth is "latitude." Latitude lines run horizontally around the globe, measuring the distance north or south of the Equator. These lines are used in geographic coordinate systems to help locate positions on the Earth's surface.