Question

δabc≅δxyz which is true? ab≅xy ab≅yx ab≅xz bc≅cb

Explanation:

Step1: Recall the property of congruent triangles

When \(\triangle ABC\cong\triangle XYZ\), the corresponding parts are congruent. That is \(AB\) corresponds to \(XY\), \(BC\) corresponds to \(YZ\), and \(AC\) corresponds to \(XZ\).

Step2: Check each option

• For the option \(AB\cong XY\): Since \(AB\) and \(XY\) are corresponding sides of congruent triangles \(\triangle ABC\) and \(\triangle XYZ\) (by the order of congruence \(\triangle ABC\cong\triangle XYZ\)), this is correct.
• For the option \(AB\cong YX\): The order of vertices in the side - name matters. In congruent triangles \(\triangle ABC\cong\triangle XYZ\), \(AB\) corresponds to \(XY\) not \(YX\).
• For the option \(AB\cong XZ\): \(AB\) corresponds to \(XY\) (not \(XZ\)) as per the congruence \(\triangle ABC\cong\triangle XYZ\).
• For the option \(BC\cong CB\): While \(BC = CB\) (by the reflexive property of equality for line - segments), this does not come from the congruence \(\triangle ABC\cong\triangle XYZ\). The congruence \(\triangle ABC\cong\triangle XYZ\) gives \(BC\cong YZ\).

Answer:

\(AB\cong XY\)