Question

A student made the table shown below to prove that MN is equal to NT.

Answer 1

Statements Justifications
RN = PN
Given
m∡PNM = m∡RNT
Given
m∡MRN = m∡TPN
Given
m∡PNT = m∡PNM + m∡MNT
Angle Addition Postulate
m∡RNM = m∡RNT + m∡MNT
Angle Addition Postulate

m∡PNT = m∡RNM
Transitive Property
RNM ≅ PNT
ASA postulate
MN = TN

CPCTC

A. Provide the missing statement and justification in the proof.
B. Using complete sentences, explain why the proof would not work without the missing step.

Answer 2

@mathstudent55

Answer 3

I can do part B, I'm stuck on part A

Answer 4

Statements Justifications
RN = PN Given
m∡PNM = m∡RNT Given
m∡MRN = m∡TPN Given
m∡PNT = m∡PNM + m∡MNT Angle Addition Postulate
m∡RNM = m∡RNT + m∡MNT Angle Addition Postulate
m∡PNT = m∡RNM Transitive Property
RNM ≅ PNT ASA postulate
MN = TN CPCTC

Answer 5

Where is the missing statement?

Answer 6

Statements Justifications
1. RN = PN Given
2. m∡PNM = m∡RNT Given
3. m∡MRN = m∡TPN Given
4. m∡PNT = m∡PNM + m∡MNT Angle Addition Postulate
5. m∡RNM = m∡RNT + m∡MNT Angle Addition Postulate
6. m∡PNT = m∡RNM Transitive Property
7. RNM ≅ PNT ASA postulate
8. MN = TN CPCTC

Answer 7

After step 5. add
m∡RNM = m∡PNM + m∡MNT Substitution