Question

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

Look at the figure shown below.

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 ≅ trianglePNT

ASA postulate

MN = TN

CPCTC

Answer 2

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