Question

congruency of triangles quick check
if ∠x≅∠l, ∠p≅∠m, ∠a≅∠k, (overline{pa}congoverline{mk}), (overline{ax}congoverline{kl}), and (overline{xp}congoverline{lm}), which option below shows a correct congruence statement? (1 point)
△pax≅△mkl
△xpa≅△klm
△xpa≅△mkl
△pax≅△klm

Explanation:

Step1: Match corresponding vertices

Given $\angle X\cong\angle L$, $\angle P\cong\angle M$, $\angle A\cong\angle K$, $\overline{PA}\cong\overline{MK}$, $\overline{AX}\cong\overline{KL}$, $\overline{XP}\cong\overline{LM}$. The order of corresponding vertices for congruent triangles should match the equal - angle and equal - side relationships.

Step2: Determine the correct congruence statement

The correct order of vertices gives $\triangle XPA\cong\triangle LMK$. But among the given options, we need to find the one that follows the correct correspondence. The correct congruence statement is $\triangle XPA\cong\triangle LMK$ which is equivalent to $\triangle XPA\cong\triangle KLM$ (since triangle naming is flexible as long as the correspondence is maintained).

Answer:

$\triangle XPA\cong\triangle KLM$