Question

based only on the information given in the diagram, it is guaranteed that △abc～△xyz. a. true b. false

Explanation:

Step1: Recall similarity criterion

Two triangles are similar if two pairs of corresponding angles are equal. In \(\triangle ABC\) and \(\triangle XYZ\), \(\angle A = 43^{\circ}\), \(\angle X=43^{\circ}\) and \(\angle C=\angle Z = 90^{\circ}\).

Step2: Apply AA - similarity

Since two pairs of corresponding angles (\(\angle A\) and \(\angle X\), \(\angle C\) and \(\angle Z\)) are equal, by the Angle - Angle (AA) similarity criterion, \(\triangle ABC\sim\triangle XYZ\).

Answer:

A. True