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Which lines of longitude and latitude vary in length?
-- All meridians of longitude have the same length ... they all join the north and south poles. -- Each parallel of north latitude has the same length as the parallel at the equal south latitude, but no other one.
Why aren't all parallels equal in length like meridians are?
There's a simple answer: The earth is a sphere and the parallels are, well, parallel to each other. So obviously the ones closer to the poles are shorter than the ones closest to the Ecuator. As for the meridians all meet at one point ehich are the poles, so they are all the same length.
Why was it necessary to specify a particular meridan when determining the length of a meter?
I don't see the need for that - all meridians (for example, at sea level) should have the same length.
What is a triangle with all three sides are equal length?
If all three sides are equal in length, the triangle is said to be Equilateral.
Are any of a octagons sides equal in length?
They can be. A regular octagon has all sides of equal length.
