Question

$\overline{qs}\cong\overline{qt}$ and $\angle p\cong\angle r$. complete the proof that $\triangle qrs\cong\triangle qpt$.

Explanation:

Step1: List given info

$\overline{QS} \cong \overline{QT}$ (Given), $\angle P \cong \angle R$ (Given)

Step2: Identify vertical angles

$\angle PQT \cong \angle RQS$ (Vertical Angle Theorem)

Step3: Apply AAS congruence

Two angles and non-included side of $\triangle QRS$ ≅ corresponding parts of $\triangle QPT$

Answer:

Angle-Angle-Side (AAS) Congruence Theorem