Question

aas proof #1 given: sr bisects ∠qst, ∠sqr = ∠str prove: △qsr = △tsr

Explanation:

Step1: State angle - bisector property

Since $\overline{SR}$ bisects $\angle QST$, we have $\angle QSR=\angle TSR$. (Definition of angle - bisector)

Step2: Identify given angle equality

We are given that $\angle SQR = \angle STR$.

Step3: Identify common side

$\overline{SR}=\overline{SR}$ (Reflexive property of congruence).

Step4: Apply AAS congruence criterion

In $\triangle QSR$ and $\triangle TSR$, we have two pairs of angles equal ($\angle QSR=\angle TSR$ and $\angle SQR = \angle STR$) and a non - included side equal ($\overline{SR}$ is common), so $\triangle QSR\cong\triangle TSR$ by the Angle - Angle - Side (AAS) congruence criterion.

Answer:

Statements	Reasons
$\angle QSR=\angle TSR$	Definition of angle - bisector
$\angle SQR = \angle STR$	Given
$\overline{SR}=\overline{SR}$	Reflexive property of congruence
$\triangle QSR\cong\triangle TSR$	AAS congruence criterion