Question

match each part of △xyz to its corresponding part in △abc. ∠x ∠y ∠z xy xz yz
ba ac bc ∠a ∠b ∠c

Explanation:

Step1: Identify angle - angle correspondences

In $\triangle XYZ$, $\angle X = 80^{\circ}$, in $\triangle ABC$, $\angle C=80^{\circ}$, so $\angle X$ corresponds to $\angle C$. In $\triangle XYZ$, $\angle Y = 30^{\circ}$, in $\triangle ABC$, $\angle A = 30^{\circ}$, so $\angle Y$ corresponds to $\angle A$. Then $\angle Z$ corresponds to $\angle B$ since the sum of angles in a triangle is $180^{\circ}$ and the remaining angles must match.

Step2: Identify side - side correspondences

Corresponding angles are opposite corresponding sides. $\overline{XY}$ is opposite $\angle Z$, and $\overline{BC}$ is opposite $\angle B$, so $\overline{XY}$ corresponds to $\overline{BC}$. $\overline{XZ}$ is opposite $\angle Y$, and $\overline{BA}$ is opposite $\angle A$, so $\overline{XZ}$ corresponds to $\overline{BA}$. $\overline{YZ}$ is opposite $\angle X$, and $\overline{AC}$ is opposite $\angle C$, so $\overline{YZ}$ corresponds to $\overline{AC}$.

Answer:

$\angle X$ - $\angle C$
$\angle Y$ - $\angle A$
$\angle Z$ - $\angle B$
$\overline{XY}$ - $\overline{BC}$
$\overline{XZ}$ - $\overline{BA}$
$\overline{YZ}$ - $\overline{AC}$