Given: SQ bisects RQT and RST Prove: QRS is congruent to QTS

Provide a reason for each given statement:
Reason 1:
Given
Reason 2:
SQ bisects the angle RQT.
Reason 3:
SQ bisects the angle RST
Reason 4:
Reflexive property of the congruence
Reason 5:
ASA criterion.
Notice that since two angles form the triangles are congruent, then RQS and TQS are similar triangles. Then, it is enough to show that they have one congruent side to prove that they are in fact more than similar, but congruent.