Question

is \\( \triangle wxz \cong \triangle yzx \\)? why or why not?
yes, they are congruent by sas.
yes, they are both right triangles.
no, the triangles share side \\( \overline{xz} \\).
no, there is only one set of congruent sides.

Explanation:

Step1: Identify the congruent sides

We have \(WX = YZ=21\) cm. Also, \(XZ\) is common to both \(\triangle WXZ\) and \(\triangle YZX\), so \(XZ = XZ\) (reflexive property).

Step2: Identify the included angles

\(\angle WXZ=\angle YZX = 90^{\circ}\)

Since we have two sides and the included angle (SAS - Side - Angle - Side) congruent for \(\triangle WXZ\) and \(\triangle YZX\)

Answer:

Yes, they are congruent by SAS.