You never placed stated that angle bad is congruent to angle cda. What would the reason for that be? Would you have to state that bad is bac + cad and the same for cda, then use the Reflexive?

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Please, if you are going to ask a question. Please put a diagram up or somehow explain what you are talking about. The rest of us have no idea what angle BAD is or CDA... All we know is that your figure has at least 4 sides which is not telling much.... Thanks!