Answer
a. Vertical angles are congruent.
b. Given
c. $\overline{TQ}$ is congruent to $\overline{RQ}$.
d. AAS postulate
Work Step by Step
a. $\angle NQT$ and $\angle SQR$ are vertical angles; therefore, they are congruent.
b. This statement was given originally.
c. If line $l$ bisects $\overline{TR}$ at $Q$, then $\overline{TQ}$ is congruent to $\overline{RQ}$.
d. Two angles and one non-included side of both triangles are congruent; therefore, the triangles are congruent by the AAS postulate.
