Question

based only on the information given in the diagram, it is guaranteed that (\triangle efgsim\triangle hjk).

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

For two right - angled triangles (both \(\triangle EFG\) and \(\triangle HJK\) have a right - angle, \(\angle E = 90^{\circ}\) and \(\angle H=90^{\circ}\)), we need at least one more pair of equal angles to prove similarity.

Step2: Check for additional angle information

The given diagram only provides the length of one side (\(EG = 8\) and \(HK = 16\)). There is no information about the other angles (\(\angle F\) and \(\angle G\) in \(\triangle EFG\), \(\angle J\) and \(\angle K\) in \(\triangle HJK\)). Just having one right - angle is not sufficient to guarantee similarity as we don't know if the other non - right angles are equal.

Answer:

B. False