f ∠x≅∠l , ∠p≅∠m , ∠a≅∠k , pa¯¯¯¯¯¯¯¯≅mk¯¯¯¯¯¯¯¯¯¯ , ax¯¯¯¯¯¯¯¯≅kl¯¯¯¯¯¯¯¯ , and xp¯¯¯¯¯¯¯¯≅lm¯¯¯¯¯¯¯¯¯ , which option below shows a correct congruence statement?(1 point)

Question

responses

△xpa≅△mkl
triangle upper x upper p upper a congruent to triangle upper m upper k upper l

△xpa≅△klm
triangle upper x upper p upper a congruent to triangle upper k upper l upper m

△pax≅△mkl
triangle upper p upper a upper x congruent to triangle upper m upper k upper l

△pax≅△klm

Answer 1

To determine the correct congruence statement, we need to examine the corresponding angles and sides of the triangles based on the given information.

1. We have the following angle congruences:

   • ∠x ≅ ∠l
   • ∠p ≅ ∠m
   • ∠a ≅ ∠k

2. We also have the following side congruences:

   • \( \overline{pa} ≅ \overline{mk} \)
   • \( \overline{ax} ≅ \overline{kl} \)
   • \( \overline{xp} ≅ \overline{lm} \)

Based on the given information, we can label the triangles:

• Triangle \( \triangle xpa \) has angles \( ∠x, ∠p, ∠a \) and sides \( \overline{xp}, \overline{pa}, \overline{ax} \).
• Triangle \( \triangle mkl \) has angles \( ∠m, ∠k, ∠l \) and sides \( \overline{lm}, \overline{mk}, \overline{kl} \).

Now, matching the angles and sides:

• Angle \( ∠x \) corresponds to \( ∠l \)
• Angle \( ∠p \) corresponds to \( ∠m \)
• Angle \( ∠a \) corresponds to \( ∠k \)

And the sides:

• \( \overline{pa} \) corresponds to \( \overline{mk} \)
• \( \overline{ax} \) corresponds to \( \overline{kl} \)
• \( \overline{xp} \) corresponds to \( \overline{lm} \)

Given this, the correct congruence statement based on corresponding parts of triangles \( \triangle xpa \) and \( \triangle mkl \) would be:

△xpa ≅ △mkl

So the correct option is: △xpa≅△mkl (triangle upper x upper p upper a congruent to triangle upper m upper k upper l).