Question

which must be true in order for the relationship δzyx ~ δwvu to be correct?

• (overline{zy} parallel overline{wv})
• (angle z cong angle y) and (angle w cong angle v)
• (overline{zy} cong overline{yx}) and (overline{wv} cong overline{vu})
• (angle z cong angle w) and (angle x cong angle u)

(diagram: two triangles, left labeled z, y, x; right labeled w, v, u)

Explanation:

For similar triangles (\(\triangle ZYX \sim \triangle WVU\)), corresponding angles must be congruent. The correct condition is \(\angle Z \cong \angle W\) and \(\angle X \cong \angle U\) (AA similarity criterion), as corresponding angles of similar triangles are equal. Other options don't satisfy similarity conditions (parallel lines don't imply similarity here, equal angles in option 2 are not corresponding, equal sides imply congruence not similarity).

Answer:

\(\boldsymbol{\angle Z \cong \angle W \text{ and } \angle X \cong \angle U}\) (the last option: \(\boldsymbol{\angle Z \cong \angle W \text{ and } \angle X \cong \angle U}\))