Question

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

Explanation:

Step1: Recall postulate conditions

SSS (Side - Side - Side) postulate requires three pairs of equal sides and SAS (Side - Angle - Side) postulate requires two pairs of equal sides and the included angle equal.
We are given $\overline{NP}=\overline{OM}$ and $\overline{MN}=\overline{PO}$. The third side $\overline{MP}$ is common to both $\triangle MNP$ and $\triangle POM$. So we have $\overline{MP}=\overline{MP}$.

Step2: Check SSS postulate

Since $\overline{NP}=\overline{OM}$, $\overline{MN}=\overline{PO}$ and $\overline{MP}=\overline{MP}$, by the SSS postulate, $\triangle MNP\cong\triangle POM$.

Step3: Check SAS postulate

There is no information given about the included angles between the equal - side pairs. So we cannot use the SAS postulate.

Answer:

by SSS only