Question

critical thinking given △abc~△def and △def~△jkl, is △abc~△jkl? yes no

Explanation:

Step1: Recall the transitive property of similarity

If \( \triangle ABC\sim\triangle DEF\), then the corresponding angles of \( \triangle ABC\) and \( \triangle DEF\) are equal. That is, \(\angle A=\angle D\), \(\angle B = \angle E\), \(\angle C=\angle F\). Also, if \( \triangle DEF\sim\triangle JKL\), then \(\angle D=\angle J\), \(\angle E=\angle K\), \(\angle F=\angle L\).

Step2: Use angle - angle similarity criterion

By substitution, \(\angle A=\angle J\), \(\angle B=\angle K\), \(\angle C=\angle L\). According to the AA (angle - angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), since all three pairs of corresponding angles of \( \triangle ABC\) and \( \triangle JKL\) are equal, \( \triangle ABC\sim\triangle JKL\).

Answer:

yes