Question

1. given: \\( \overline { m n } \cong \overline { p o } , \overline { m p } \cong \overline { n o } \\)

prove: \\( \delta p m n \cong \delta n o p \\)

Explanation:

Step1: Identify the common side

In \(\triangle PMN\) and \(\triangle NOP\), \(PN = NP\) (reflexive property of congruence).

Step2: List the given congruent sides

We are given \(MN\cong PO\) and \(MP\cong NO\).

Step3: Apply SSS (Side - Side - Side) congruence criterion

Since \(MN\cong PO\), \(MP\cong NO\), and \(PN = NP\), by the SSS congruence criterion, \(\triangle PMN\cong\triangle NOP\).

Answer:

Statement	Reason
\(MP\cong NO\)	Given
\(PN = NP\)	Reflexive property of congruence
\(\triangle PMN\cong\triangle NOP\)	SSS (Side - Side - Side) congruence criterion