Question

Question

If ∠X≅∠L
, ∠P≅∠M
, ∠A≅∠K
, PA¯¯¯¯¯¯¯¯≅MK¯¯¯¯¯¯¯¯¯¯
, AX¯¯¯¯¯¯¯¯≅KL¯¯¯¯¯¯¯¯
, and XP¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯
, which option below shows a correct congruence statement?(1 point)
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≅△KLM
triangle upper P upper A upper X congruent to triangle upper K upper L upper M

△PAX≅△MKL

Answer 1

To determine which triangle congruence statement is correct based on the provided angle and side congruences, we can use the information given about the angles and sides.

1. Given Congruences:

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

2. Triangle Congruence Criteria: The triangles can be shown to be congruent based on the Angle-Side-Angle (ASA) or Side-Side-Side (SSS) criteria.

3. Analyzing the Options:

   • Option 1: △XPA ≅ △MKL

     • This is valid because:
       • ∠X ≅ ∠L
       • PA ≅ MK
       • ∠A ≅ ∠K
     • This fits the ASA congruence criteria.

   • Option 2: △XPA ≅ △KLM

     • This is not valid since it doesn't fit our given congruences correctly.

   • Option 3: △PAX ≅ △KLM

     • This is not valid since it doesn’t follow our provided congruences.

   • Option 4: △PAX ≅ △MKL

     • This is also not valid since it doesn’t follow our provided congruences.

4. Correct Choice: From the analysis, the correct option showing a valid congruence statement is:

△XPA ≅ △MKL.

This is due to the congruences of the angles and the sides that hold true as per the given information.