geometry help needed, please

Why is line segment ab = line segment ab? what is the name of the reason/postulate/whatever it is called?

Also, if you know that you have 2 triangles and you are trying to prove they are congruent and you know that 2 sides are equal and 1 angle is equal, which reason/law/postulate do you cite?

Thank you!

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geometry help needed, again

If you have 2 line segments, which form the 2 sides of a traingle, and have been given the fact that corresponding segments of the sides are equal, what rule could you cite to prove that the entire length of the 2 sides are the same.

I am eventually trying to prove that the triangle is isosceles.

A diagram is attached.

Thanks!