Answer:
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Explanation:
In triangle ABC, if AB = AC and <BAD = <CAD, then we can conclude that triangle ABD and triangle ACD are congruent by the angle-side-angle (ASA) postulate.
Specifically, we have:
AB = AC (given)
<BAD = <CAD (given)
AD is a common side to both triangles
Therefore, the two triangles have two congruent angles and the included side AD is the same for both. As a result, the other sides of the triangles must also be congruent, which means:
BD = CD (by the side-side-side (SSS) congruence)
AB = AC (given)
Since opposite sides in a parallelogram are equal, we can conclude that BD and AC are parallel and have the same length. Similarly, CD and AB are parallel and have the same length. Therefore, we have a parallelogram ABCD, and we can conclude that AD is equal to BC, because opposite sides of a parallelogram are equal in length.
Therefore, we have:
AD = BC