13. Developing Proof Complete the two-column proof by filling in the blanks.
Given: $\angle N \cong \angle S$, line $\ell$ bisects $\overline{T R}$ at $Q$
Prove: $\triangle N Q T \cong \triangle S Q R$
Statements
Reasons
1) $\angle N \cong \angle S$
1) Given
2) $\angle N Q T \cong \angle S Q R$
2) a. ?
3) Line $\ell$ bisects $\overline{T R}$ at $Q$.
3) b. ?
4) c. ?
4) Definition of bisect
5) $\triangle N Q T \cong \triangle S Q R$
5) d. ?
Answer
5) By ASA postulate, \(\triangle N Q T \cong \triangle S Q R\)
Step 1 ：1) Given: \(\angle N \cong \angle S\)
Step 2 ：2) Vertical angles are congruent, so \(\angle N Q T \cong \angle S Q R\)
Step 3 ：3) Given: Line \(\ell\) bisects \(\overline{T R}\) at \(Q\)
Step 4 ：4) By definition of bisect, \(\overline{T Q} \cong \overline{Q R}\)
Step 5 ：5) By ASA postulate, \(\triangle N Q T \cong \triangle S Q R\)
