Question

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

Explanation:

Step1: Analyze the given information

We are given two triangles \(\triangle WXZ\) and \(\triangle YZX\). We know that \(WX = YZ=21\mathrm{cm}\).

Step2: Check the congruence criteria

For SAS (Side - Angle - Side) congruence, we need two sides and the included angle to be congruent. Just knowing one pair of sides (\(WX = YZ\)) is not sufficient. Also, sharing a side (\(XZ\)) is not a valid reason for non - congruence. Being right triangles (\(\angle WXZ=\angle YZX = 90^{\circ}\)) only gives us one angle, but we still lack information about other sides and angles. Since we only have one set of congruent sides (\(WX = YZ\)) and no other information about congruent sides or angles (except the right angles which are not enough for congruence without more side - angle relations), the triangles are not congruent.

Answer:

No, there is only one set of congruent sides.