Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: $overline{lp}congoverline{np}$, $angle mlpcongangle onp$, $angle lmpcongangle nop$. prove: $\triangle lmpcong\triangle nop$

Explanation:

Step1: Identify given congruences

We are given $\overline{LP}\cong\overline{NP}$, $\angle MLP\cong\angle ONP$, and $\angle LMP\cong\angle NOP$.

Step2: Recall congruence postulates

The AAS (Angle - Angle - Side) postulate states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Step3: Apply the postulate

In $\triangle LMP$ and $\triangle NOP$, we have two pairs of congruent angles ($\angle MLP\cong\angle ONP$ and $\angle LMP\cong\angle NOP$) and a pair of congruent non - included sides ($\overline{LP}\cong\overline{NP}$). So, by AAS, $\triangle LMP\cong\triangle NOP$.

Answer:

The Angle - Angle - Side (AAS) Theorem justifies the proof that $\triangle LMP\cong\triangle NOP$.