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Postulate 13 (SSS Postulate): If each side of one triangle is congruent to the corresponding side of another triangle, then the triangles are congruent
Side-Side-Side. Simply, If the corresponding sides have equal measure, the triangles are congruent.
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Postulate 14 (SAS Postulate): If two sides and the angle between them in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent
Side-Angle-Side.

Lets say the letters correspond to ONE value only. Lets say A has a value of X and a has a value of Y. You can only get X as the value of A if the value of a is Y(since a intersects A). Same goes with the other sides/angles.
For instance, we are given only A, B, and c(wherein c determines the length of C), and the second triangle have the same measures for the corresponding sides/angle. Therefore A
1=A
2, B
1=B
2, c
1=c
2 wherein c determines the length of C. That means the angle will result into the
same length of the third side. If we were to go back to postulate 13, the triangles are congruent.
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Postulate 15 (ASA Postulate): If two angles and the side between them in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent
Angle-Side-Angle
Two angle measures are given, which means we can find the last angle measure -- 180-(A
1+A
2), since the measure of all interior angles in a triangle is equal to 180. If two are given, we can presume that the corresponding angles with unknown values are equal. Since the angles determines the sides, and with the given situation, three sides are congruent. Postulate 13.
BUT WAIT! What about the side stated?
AFAIK, it tells about the correspondence of sides/angles of a triangle.
ugh. Sorry, this is all what i can pull out of my mind. I'm taking our quarterly exams atm, so i have other subject matter fluttering in my mind. @.@