Question

$\triangle abc\cong \triangle xyz$ which is true? ab$\cong$yx; bc$\cong$cb; ab$\cong$xy; ab$\cong$xz

Explanation:

Step1: Recall congruent triangle properties

In congruent triangles, corresponding sides are congruent. For \(\triangle ABC \cong \triangle XYZ\), the order of the vertices matters. So vertex \(A\) corresponds to \(X\), \(B\) corresponds to \(Y\), and \(C\) corresponds to \(Z\).

Step2: Analyze each option

• Option 1 (\(AB \cong YX\)): \(AB\) corresponds to \(XY\) (not \(YX\)), so this is false.
• Option 2 (\(BC \cong CB\)): This is about the same segment (reflexive property), but it doesn't relate to the congruent triangles \(\triangle ABC\) and \(\triangle XYZ\), so it's not relevant here.
• Option 3 (\(AB \cong XY\)): Since \(A\) corresponds to \(X\) and \(B\) corresponds to \(Y\), side \(AB\) (between \(A\) and \(B\)) corresponds to side \(XY\) (between \(X\) and \(Y\)), so \(AB \cong XY\) is true.
• Option 4 (\(AB \cong XZ\)): \(AB\) corresponds to \(XY\) (not \(XZ\), as \(Z\) corresponds to \(C\)), so this is false.

Answer:

C. \(AB \cong XY\) (assuming the orange option is labeled as C, with the text \(AB \cong XY\))