14. in congruent triangles, if the side - length of $ \triangle x y z $ is given as x, y, z and for $ \triangle a b c $ is a, b, c, which sas condition is correct? $ x = a, \angle z \cong \angle c, y = b $ $ z = c, \angle z \cong \angle c, y = b $ $ x = a, \angle a \cong \angle x, a = x $ $ x = z, \angle y \cong \angle b, a = c $

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# Brief Explanations:
To determine the correct SAS (Side - Angle - Side) condition for congruent triangles $\triangle XYZ$ (with sides $x,y,z$) and $\triangle ABC$ (with sides $a,b,c$), we recall that the SAS criterion requires two sides and the included angle of one triangle to be congruent to the corresponding two sides and the included angle of the other triangle.

1. Analyze the first option: $x = a$, $\angle Z\cong\angle C$, $y = b$. The angle $\angle Z$ is not the included angle between sides $x$ and $y$ in $\triangle XYZ$ (the included angle between $x$ and $y$ would be $\angle Y$ or $\angle X$ depending on the labeling), so this does not satisfy SAS.
2. Analyze the second option: $z = c$, $\angle Z\cong\angle C$, $y = b$. In $\triangle XYZ$, the sides adjacent to $\angle Z$ are $y$ and $z$, and in $\triangle ABC$, the sides adjacent to $\angle C$ are $b$ and $c$. So we have two sides ($z = c$ and $y = b$) and the included angle ($\angle Z\cong\angle C$) which satisfies the SAS congruence criterion.
3. Analyze the third option: $x = a$, $\angle A\cong\angle X$, $a = x$. This is a repetition of $x=a$ and the angle $\angle A$ and $\angle X$ are not the included angles between the sides that are supposed to be equal ($x$ and $a$ are the same side), so this does not satisfy SAS.
4. Analyze the fourth option: $x = z$, $\angle Y\cong\angle B$, $a = c$. The sides $x,z$ in $\triangle XYZ$ and $a,c$ in $\triangle ABC$ are not corresponding sides in a way that would satisfy SAS, and the angle - side relationship is incorrect.

# Answer:
The correct option is the second one: $z = c$, $\angle Z\cong\angle C$, $y = b$

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