Answer: B. False
Step-by-step explanation:
In the given picture, we have two right triangles Δ PQR and Δ STU righta angled at ∠P and ∠ S respectively.
Also, it is shown that QR=6 units and TU =12 units.
Since, we have given only one pair of congruent angles, thus we cannot apply AA postulate of similarity to it.
Also, we have only one pair of corresponding sides, so we cannot check the proportionality of the corresponding sides.
Therefore, it is false that "based only on the information given in the diagram it is guaranteed that triangle PQR ~triangle STU" because they may might be not similar if their corresponding angles are actually different.
