A congruent D; AB congruent DE; B congruent E
ABC congruent DEF- ASA postulate
Statement involving segments or line segments, where D, AB, DE, B, and E are points or line segments.
The statement A congruent D means that point A is congruent to point D. Congruent means that they have the same shape and size, so they perfectly overlap each other.
The statement AB congruent DE means that line segment AB is congruent to line segment DE. Again, congruent means that they have the same length and shape, so they would perfectly overlap each other.
The statement B congruent E means that point B is congruent to point E. Similarly to the first statement, this means that they have the same shape and size, so they would perfectly overlap each other.
Taken together, these three statements imply that there exists a transformation (such as a translation, rotation, reflection or combination of those) that maps point A to point D, line segment AB to line segment DE, and point B to point E. We call this a congruence transformation, and it preserves lengths, angles, and shapes.
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