Question

triangle xyz was translated up 2 and right 3 units, creating triangle cab. which relationship between the parts of the two triangles must be true? ∠x≅∠a ∠zx≅∠ca ∠yz≅∠ab ∠z≅∠c

Explanation:

Step1: Recall translation property

Translation is a rigid - motion. Rigid - motions preserve side - lengths and angle - measures. Corresponding parts of translated figures are congruent.

Step2: Identify corresponding parts

When $\triangle XYZ$ is translated to $\triangle CAB$, the vertices correspond as follows: $X$ corresponds to $C$, $Y$ corresponds to $A$, and $Z$ corresponds to $B$.

Step3: Analyze angle congruence

For angles, $\angle Z$ corresponds to $\angle B$, $\angle X$ corresponds to $\angle C$, and $\angle Y$ corresponds to $\angle A$. For sides, $\overline{ZX}$ corresponds to $\overline{CB}$, $\overline{YZ}$ corresponds to $\overline{AB}$, and $\overline{XY}$ corresponds to $\overline{CA}$.

Answer:

C. $\overline{YZ}\cong\overline{AB}$