Question

Given: QS bisects ∠TQR; TQ ≅ RQ.

Prove: ΔQRS ≅ ΔQTS
Complete the missing parts of the paragraph proof.

Proof:
We know that segment QS bisects angle TQR because __________. By the definition of angle bisector, angle TQS is congruent to angle __________. We see that segment QS is congruent to segment SQ by ___________. Therefore, we can conclude that triangles QRS and QTS are congruent by____________

Answer 1

We know that segment QS bisects angle TQR because it is given. By the definition of angle bisector, angle TQS is congruent to angle RQS. We see that segment QS is congruent to segment SQ by the reflexive property. Therefore, we can conclude that triangles QRS and QTS are congruent by SAS.

Answer 2

it is given,
rqs,
the reflexive property,
sas