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You can put this solution on YOUR website! This same question identically was asked two more times. This response will not be a formal proof, but just a helpful description.
You know that AB contains the collinear points D and E, and that AB is a segment, forming supplementary angles at D and at E. You know from this that angles ADC and BEC are congruent,... something about supplementary angles of congruent angles...
You have at least, these ... statements:
AD congru BE | Given
angles CDE congru CED | Given
angles ADC congru BEC | Reason discussed above
Triangles ADC and BEC congruent | Not know how to state this theorem, but two sides and included angles....
Segments AC congru BC | Corresponding parts of congruent triangles...
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