Question

which additional fact would prove △pqr≅△stu? a. ∠p≅∠s b. ∠q≅∠t c. ∠r≅∠s d. ∠r≅∠u

Explanation:

Step1: Recall congruence criteria

For two triangles to be congruent, we have criteria like SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) and HL (Hypotenuse - Leg for right - triangles). Here we already have two pairs of sides equal. We need an included - angle or another pair of angles to prove congruence.

Step2: Analyze the options

Option A ($\angle P\cong\angle S$) is not correct as these are not the included angles between the equal sides. Option B ($\angle Q\cong\angle T$) is correct because if we have two pairs of sides equal and the included angles between them equal (by $\angle Q\cong\angle T$), we can use the SAS (Side - Angle - Side) congruence criterion to prove $\triangle PQR\cong\triangle STU$. Option C ($\angle R\cong\angle S$) and Option D ($\angle R\cong\angle U$) are not the correct angles for the known side - side equalities to prove congruence.

Answer:

B. $\angle Q\cong\angle T$