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On a number of posts, like this, I have seen people state that a triangle is "in AP". Can someone explain what that abbreviation stands for in this context?

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    Arithmetic Progression is often abbreviated that way and is not ambiguous anywhere. – 2017-01-05
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    Arithmetic progession. Cite: I googled and found http://math.stackexchange.com/questions/883612/trigonometric-ap-relation-on-sides-of-a-triangle – 2017-01-05

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Here it means arithmetic progression, so if the sides are $a,b,c$ we have $a+d=b, b+d=c$ for some $d$. You also see GP for geometric progrssion.

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    Does proving that a triangle is in AP or GP have any significant meaning? Can we use these definitions to prove other things about the triangles? – 2017-01-05
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    I don't know of one. – 2017-01-05