Question

what is the missing reason in the proof?

Explanation:

Step1: Analyze the given equal angles

We know that \(\angle2\cong\angle3\) (from step 2, alternate - interior angles theorem as \(\overline{NM}\parallel\overline{PO}\)) and \(\angle1\cong\angle3\) (from step 3, given).

Step2: Use the transitive property of congruence

The transitive property of congruence states that if \(a = b\) and \(b = c\), then \(a = c\). Here, if we let \(a=\angle1\), \(b = \angle3\), and \(c=\angle2\) (since \(\angle2\cong\angle3\) and \(\angle1\cong\angle3\)), we can get \(\angle1\cong\angle2\).

Answer:

transitive property of congruence