Questions: Consider the diagram. The congruence theorem that can be used to prove triangle MNP congruent to triangle ABC is - SSS. - ASA. - SAS.

Solution Steps

The diagram shows two triangles, $\triangle MNP$ and $\triangle ABC$. We are given that segment $AM$ is congruent to segment $PN$, segment $NB$ is congruent to segment $MB$, and angle $\angle MNB$ is congruent to angle $\angle ABC$. We are asked to determine the appropriate congruence theorem.

We are given two pairs of congruent sides and a pair of congruent angles. The congruent angles are $\angle MNB$ and $\angle ABC$. The congruent sides are $MB \cong NB$ and $AM \cong PN$. Since $AM + MB = AB$ and $PN + NB = MN$, and $AM \cong PN$ and $MB \cong NB$, we know that $AB \cong MN$. This means we have two pairs of congruent sides $AB \cong MN$ and $NB \cong MB$ and the included congruent angles $\angle ABC \cong \angle MNB$. Therefore, the triangles are congruent by SAS.

Final Answer: SAS