Question

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

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 1

@Mertsj

Answer 2

@ParthKohli @dpaInc

Answer 3

measure angle RNM=measure angle PNM + measure angle MNT by substitution

Answer 4

The proof doesn't work without the missing step because the transitive property says "if a = b and b = c then a = c. Therefore the proof must contain statements that one quantity is equal to two different quantities or the transitie property cannot be used.