Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: $overline{lp}congoverline{np}$, $overline{lo}congoverline{nm}$, $overline{op}congoverline{mp}$; prove: $\triangle lpocong\triangle npm$

Explanation:

Step1: Identify congruent sides

We are given $\overline{LP}\cong\overline{NP}$, $\overline{LO}\cong\overline{NM}$, and $\overline{OP}\cong\overline{MP}$.

Step2: Recall congruence postulates

The SSS congruence postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step3: Apply postulate

In $\triangle LPO$ and $\triangle NPM$, the three pairs of corresponding sides are congruent, so by the SSS Congruence Postulate, $\triangle LPO\cong\triangle NPM$.

Answer:

Side - Side - Side (SSS) Congruence Postulate