Question

if △jkl ≅ △mnp, which statement must be true?
a. $overline{jk}congoverline{mp}$
b. $overline{jk}congoverline{kl}$
c. $angle kcongangle n$
d. $angle kcongangle m$

Explanation:

Step1: Recall congruent - triangle property

When $\triangle{JKL}\cong\triangle{MNP}$, corresponding angles and corresponding sides are congruent. The order of the vertices in the congruence statement indicates the corresponding parts.

Step2: Analyze each option

• Option A: $\overline{JK}$ corresponds to $\overline{MN}$, not $\overline{MP}$, so $\overline{JK}

ot\cong\overline{MP}$.

• Option B: $\overline{JK}$ and $\overline{KL}$ are sides of the same triangle $\triangle{JKL}$, and we cannot say they are congruent just because $\triangle{JKL}\cong\triangle{MNP}$.
• Option C: $\angle K$ in $\triangle{JKL}$ corresponds to $\angle N$ in $\triangle{MNP}$ since the order of vertices in $\triangle{JKL}\cong\triangle{MNP}$ gives the corresponding - angle relationships. So $\angle K\cong\angle N$.
• Option D: $\angle K$ corresponds to $\angle N$, not $\angle M$, so $\angle K

ot\cong\angle M$.

Answer:

C. $\angle K\cong\angle N$