Question

consider \\( \triangle wxy \\) and \\( \triangle bcd \\) with \\( \angle x \cong \angle c, \overline{wx} \cong \overline{bc} \\), and \\( \overline{wy} \cong \overline{bd} \\).
can it be concluded that \\( \triangle wxy \cong \triangle bcd \\) by sas? why or why not?
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
no, because the
third
corresponding
sides must also
begiven as
congruent

Explanation:

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

The SAS congruence criterion states that for two triangles to be congruent by SAS, two sides and the included angle of one triangle must be congruent to the corresponding two sides and the included angle of the other triangle.

Step2: Analyze the given congruences

We are given \(\angle X\cong\angle C\), \(\overline{WX}\cong\overline{BC}\), and \(\overline{WY}\cong\overline{BD}\). The angle \(\angle X\) is not included between \(\overline{WX}\) and \(\overline{WY}\) in \(\triangle WXY\), and the angle \(\angle C\) is not included between \(\overline{BC}\) and \(\overline{BD}\) in \(\triangle BCD\).

Answer:

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