Question

in the diagram below, \\(overline{wx} \cong overline{zy}\\).
which additional piece of information is required to conclude that \\(\triangle wyz\\) and \\(\triangle ywx\\) are congruent by side - side - side triangle congruence?
\\(overline{wz} \cong overline{xy}\\)
\\(wz > xy\\)
\\(mangle z < 90^circ\\)
\\(angle x\\) is a right angle

Explanation:

Step1: Identify given congruent sides

Given $\overline{WX} \cong \overline{ZY}$, and both triangles share $\overline{WY}$ (so $\overline{WY} \cong \overline{WY}$ by reflexive property).

Step2: Match SSS congruence requirement

SSS needs all three pairs of corresponding sides congruent. The missing pair is $\overline{WZ} \cong \overline{XY}$.

Step3: Eliminate incorrect options

• $WZ > XY$ is an inequality, not congruence.
• $m\angle Z < 90^\circ$ and $\angle X$ being a right angle relate to angles, not SSS.

Answer:

$\overline{WZ} \cong \overline{XY}$