Question

the proof that △mng ≅ △kjg is shown. given: ∠n and ∠j are right angles; ng ≅ jg. prove: △mng ≅ △kjg. what is the missing reason in the proof? statement reason 1. ng ≅ jg 1. given 2. ∠n and ∠j are right angles 2. given 3. ∠mgn ≅ ∠kgj 3. vert. ∠s are ≅ 4. ∠n ≅ ∠j 4. rt. ∠s are ≅ 5. △mng ≅ △kjg 5.? the reflexive property asa aas the third - angle theorem

Explanation:

Step1: Recall triangle - congruence postulates

We know that ASA (Angle - Side - Angle) requires two pairs of congruent angles and the included side congruent, AAS (Angle - Angle - Side) requires two pairs of congruent angles and a non - included side congruent.

Step2: Analyze given congruent parts

We are given that $\overline{NG}\cong\overline{JG}$ (a side), $\angle N\cong\angle J$ (right - angles) and $\angle MGN\cong\angle KGJ$ (vertical angles). The side $\overline{NG}$ and $\overline{JG}$ is non - included between $\angle N$ and $\angle MGN$, and $\angle J$ and $\angle KGJ$ respectively.

Answer:

C. AAS