Question

The proof that MNG ≅ KJG is shown.

Given: angle N and angle J are right angles; NG ≅ JG
Prove: MNG ≅ KJG

What is the missing reason in the proof?

the reflexive property
ASA
AAS
the third angle theorem

Answer 1

ASA theorem is the missing proof

Answer 2

The line $\mathbf{\overline{MK}}$ is a bisector of the line $\mathbf{\overline{JN}}$, and both lines form part of

ΔMNG and ΔKJG.

Correct response:

• The missing reason in the proof is; ASA

Method used to prove ΔMNG ≅ ΔKJG, and find the missing reason

A two column proof is presented as follows;

Statement ${}$                                     Reasons

1. $\overline{NG}$ ≅ $\overline{JG}$                       1. Given (hash marks representing equal length)

2. ∠N and ∠J are right angles      2. Given (symbol for right angle)

3. ∠MGN ≅ ∠KGJ                       3. Vertical angle are congruent (theorem)

4. ∠N ≅ ∠J                                   4. Right angles are (all) congruent

5. ΔMNG ≅ ΔKJG                    5. Angle-Side-Angle, ASA, congruency rule

• The missing reason in the proof is; ASA

According to the ASA congruency rule, if two angles and the included

side of one triangle are the same to two angles and the included side of

another triangle, the two triangles are congruent.

∠N, side $\mathbf{\overline{NG}}$∠MGN in ΔMNG are congruent to ∠J, side $\mathbf{\overline{JG}}$∠KGJ in ΔKJG

Therefore;

• ΔMNG ≅ ΔKJG by ASA congruency rule

Learn more about ASA postulate here:

https://brainly.com/question/4086839