Question

is △wxz ≅ △yzx? why or why not?
no, there is only one set of congruent sides.
yes, they are congruent by sas.
no, the triangles share side xz.
yes, they are both right triangles.

Explanation:

Step1: Identify congruent sides

We have \( WX = ZY=21\mathrm{cm}\) and \( XZ\) is common to both \(\triangle WXZ\) and \(\triangle YZX\). So \( XZ = XZ\) (reflexive property of equality).

Step2: Identify congruent angles

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

By the Side - Angle - Side (SAS) congruence criterion (two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle), \(\triangle WXZ\cong\triangle YZX\)

Answer:

Yes, they are congruent by SAS.