Question

1. suppose $overline{np}congoverline{om}$ and $overline{mn}congoverline{po}$. can you use the sss postulate or the sas postulate to prove $\triangle mnpcong\triangle pom$? neither apply both apply by sss only by sas only

Explanation:

Step1: Recall postulate requirements

SSS (Side - Side - Side) postulate requires three pairs of congruent sides. SAS (Side - Angle - Side) postulate requires two pairs of congruent sides and the included angle between them to be congruent.

Step2: Analyze given side - congruences

We are given $\overline{NP}\cong\overline{OM}$ and $\overline{MN}\cong\overline{PO}$. Also, $\overline{MP}\cong\overline{PM}$ (common side). So we have three pairs of congruent sides: $NP = OM$, $MN=PO$, $MP = PM$. This satisfies the SSS postulate.

Step3: Check SAS postulate

There is no information given about the included angles between the pairs of sides. So we cannot use the SAS postulate.

Answer:

C. by SSS only