Question

which is the correct congruence statement if \\( \angle a = \angle x, \angle b = \angle y \\), and \\( \angle c = \angle z \\) in triangles \\( abc \\) and \\( xyz \\)?
\\( \triangle abc \cong \triangle zyx \\)
\\( \triangle abc \cong \triangle yxz \\)
\\( \triangle abc \cong \triangle xyz \\)
\\( \triangle abc \cong \triangle xzy \\)

Explanation:

Step1: Match the corresponding angles

Given \( \angle A=\angle X\), \( \angle B = \angle Y\), \( \angle C=\angle Z\). In congruence statements, the order of the letters should correspond to the congruent angles.

Step2: Write the congruence statement

For triangle \(ABC\) and \(XYZ\), since \(A\) corresponds to \(X\), \(B\) corresponds to \(Y\), and \(C\) corresponds to \(Z\), the congruence statement is \( \triangle ABC\cong\triangle XYZ\)

Answer:

\(\triangle ABC\cong\triangle XYZ\) (the third option)