Question

in the diagram below, △abc≅△xyz. which statement must be true? cb¯≅xz¯ ∠c≅∠y ac¯≅yz¯ ∠a≅∠x

Explanation:

Step1: Recall congruent - triangle property

When \(\triangle ABC\cong\triangle XYZ\), corresponding angles and corresponding sides are congruent. The order of the letters in the triangle - congruence statement gives the corresponding parts. That is, \(A\) corresponds to \(X\), \(B\) corresponds to \(Y\), and \(C\) corresponds to \(Z\).

Step2: Analyze each option

• For \(\overline{CB}\cong\overline{XZ}\), \(CB\) corresponds to \(ZY\) not \(XZ\).
• For \(\angle C\cong\angle Y\), \(\angle C\) corresponds to \(\angle Z\) not \(\angle Y\).
• For \(\overline{AC}\cong\overline{YZ}\), \(AC\) corresponds to \(XZ\) not \(YZ\).
• For \(\angle A\cong\angle X\), since \(\triangle ABC\cong\triangle XYZ\), the corresponding angles \(\angle A\) and \(\angle X\) are congruent.

Answer:

\(\angle A\cong\angle X\)