Question

question 4 of 5 select the correct answer from each drop - down menu. consider △pnm and △pno. since $overline{pn}congoverline{pn}$ by the reflexive property of congruence, then △pnm is congruent to △pno by the sas congruence criterion. by △pno using only rigid t transitive property reflexive property cross $overline{pn}$ it maps onto △pno. since △pnm can be mapped onto the congruence criterion.

Explanation:

Step1: Recall congruence properties

The reflexive property of congruence states that any geometric figure is congruent to itself. Here, the line - segment $\overline{PN}$ is congruent to itself ($\overline{PN}\cong\overline{PN}$). This is a key part of showing that $\triangle PNM$ and $\triangle PNO$ are congruent by the Side - Angle - Side (SAS) congruence criterion. In the SAS criterion, we need two pairs of congruent sides and the included angle to be congruent. The fact that $\overline{PN}$ is common to both triangles and is congruent to itself (by reflexive property) helps in establishing the congruence of the two triangles.

Answer:

The first drop - down menu should be "reflexive property" and the second drop - down menu should be "SAS" as the reasoning for $\triangle PNM\cong\triangle PNO$ is based on the reflexive property of the common side $\overline{PN}$ and the other congruent sides and included angles which satisfy the SAS congruence criterion.