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Any two angles of a triangle determine the third angle. As a result, the side angle angle theorem is equivalent to the angle side angle theorem.
It is no more nor less important than any other theorem for congruence.
Such is called an exterior angle. A useful theorem is that an exterior angle is equal to the sum of its non adjacent interior angles.
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An example is Pythagoras's Theorem: that the sum of the squares of the two shorter side lengths of a triangle with a right-angle is equal to the square of the length of the side opposite the right angle.