Question

2.) given: ( nocong op, mocong so ) prove: ( \triangle moncong\triangle sop ) statement a.) ( angle nomcongangle pos ) d.) reason b.) c.) e.)

Explanation:

Step1: State the given information

Given \(NO\cong OP\) and \(MO\cong SO\).

Step2: Identify vertical angles

\(\angle NOM\) and \(\angle POS\) are vertical angles. By the Vertical Angles Theorem, \(\angle NOM\cong\angle POS\).

Step3: Apply the Side - Angle - Side (SAS) congruence criterion

In \(\triangle MON\) and \(\triangle SOP\), we have \(NO = OP\) (given), \(\angle NOM=\angle POS\) (vertical angles are congruent), and \(MO = SO\) (given). So, by the SAS congruence criterion, \(\triangle MON\cong\triangle SOP\).

Answer:

A. \(NO\cong OP\), \(MO\cong SO\)
B. Given
C. Vertical Angles Theorem
D. \(\triangle MON\cong\triangle SOP\)
E. Side - Angle - Side (SAS) congruence criterion