To determine the correct congruence statement, we can use the given angle and side congruences. We have:
1. ∠X ≅ ∠L
2. ∠P ≅ ∠M
3. ∠A ≅ ∠K
4. PA ≅ MK
5. AX ≅ KL
6. XP ≅ LM
From this information, we can use the Angle-Side-Angle (ASA) congruence criterion or the Side-Side-Side (SSS) criterion if all sides are also matched correctly.
The corresponding angles and sides are as follows:
- ∠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
Now, let’s analyze the given response options:
1. **△XPA≅△KLM**
- This statement matches angles and sides: ∠X ≅ ∠L, ∠P ≅ ∠M, and side PA ≅ MK, but does not incorporate the side AX or XP.
2. **△XPA≅△MKL**
- This statement attempts to match angles and sides, but the angles and sides do not correspond correctly.
3. **△PAX≅△MKL**
- This statement also does not correspond to the proper match of angles and sides.
4. **△PAX≅△KLM**
- This statement again does not align the angles and sides correctly.
The correct congruence statement based on the angle and side correspondences provided is:
**△XPA≅△KLM**
Thus, the answer is:
**△XPA≅△KLM**