Question

Triangle PNT is an obtuse angled triangle. Side PN of the triangle is extended till R so that PN is equal to NR. M is a point below T. Points M and Rand points M and N are joined using straight lines. Angle NPT is equal to angle NRM. Angle RNT is equal to angle MNP.
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
triangleRNM ≅ trian