If ∠X≅∠L , ∠P≅∠M , ∠A≅∠K , PA¯¯¯¯¯¯¯¯≅MK¯¯¯¯¯¯¯¯¯¯ , AX¯¯¯¯¯¯¯¯≅KL¯¯¯¯¯¯¯¯ , and XP¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯ , which option below shows a correct congruence statement?

Answer 1

To determine the correct congruence statement based on the given information, we can use the corresponding angles and sides that are congruent.

Given:

• ∠X ≅ ∠L
• ∠P ≅ ∠M
• ∠A ≅ ∠K
• PA ≅ MK
• AX ≅ KL
• XP ≅ LM

Based on this information, we can identify that triangles \( \triangle XPA \) and \( \triangle LMP \) are congruent. The corresponding parts of the triangles are:

• ∠X corresponds to ∠L
• ∠P corresponds to ∠M
• ∠A corresponds to ∠K
• Side PA corresponds to side MK
• Side AX corresponds to side KL
• Side XP corresponds to side LM

Thus, the correct congruence statement for the triangles is:

\[ \triangle XPA \cong \triangle LMP \]

This reflects the congruency of the corresponding angles and sides as given in your information.