Consider \( \triangle W X Y \) and \( \triangle B C D \) with \( \angle X \cong \angle C, \overline{W X} \cong \overline{B C} \), and \( \overline{W Y} \cong \overline{B D} \). Can it be concluded that \( \triangle W X Y \cong \triangle B C D \) by SAS? Why or why not? no, because the third corresponding sides must also be given as congruent no, because the corresponding congruent angles listed are not the included angles no, because all corresponding angles must be given as congruent yes, because two corresponding sides and a corresponding angle are congruent

No, because the corresponding congruent angles listed are not the included angles. In the SAS (Side-Angle-Side) condition, the angle must be the one formed by the two sides being compared. Here, while \( \angle X \cong \angle C \) is congruent, it isn't the angle that's included between the sides \( \overline{W X} \) and \( \overline{W Y} \) or \( \overline{B C} \) and \( \overline{B D} \). Yes, because two corresponding sides and a corresponding angle are congruent. Utilizing the information given, the triangles share two sides that are equal in length and one angle between those sides. According to the SAS postulate, this is a valid condition to determine that \( \triangle WXY \) is indeed congruent to \( \triangle BCD \).