Problem
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. ?
Solution
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, \(\triangle N Q T \cong \triangle S Q R\)
