Question 1186350
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It's rather bizarre to ask for an indirect proof, since a direct proof is so easy.<br>
But if that's what you need, we can do it that way.<br><pre>
BC and DC are not congruent                assumption
AB is congruent to AD                      given
angle ABC is congruent to angle DAC        given
angle B is congruent to angle D            angles opposite congruent sides are congruent
triangle BAC is congruent to triangle DAC  Angle-Side-Angle
BC is congruent to DC                      corresponding parts of congruent triangles</pre>
That contradicts the assumption, so the assumption is false; BC is congruent to DC<br>