Question

consider ( \triangle wxy ) and ( \triangle bcd ) with ( angle xcongangle c,overline{wx}congoverline{bc} ), and ( overline{wy}congoverline{bd} ). can it be concluded that ( \triangle wxycong\triangle bcd ) 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

Explanation:

Step1: Recall the SAS (Side - Angle - Side) criterion

For the SAS congruence criterion, the angle must be the included angle between the two sides.

Step2: Analyze the given sides and angle

In \(\triangle WXY\) and \(\triangle BCD\), we have \(WX\cong BC\), \(WY\cong BD\), and \(\angle X\cong\angle C\). But \(\angle X\) is not the included angle between \(WX\) and \(WY\) in \(\triangle WXY\), and \(\angle C\) is not the included angle between \(BC\) and \(BD\) in \(\triangle BCD\). So, we cannot use the SAS criterion to conclude that \(\triangle WXY\cong\triangle BCD\).

Answer:

no, because the corresponding congruent angles listed are not the included angles