To determine the correct congruence statement among the given options, we can use the information provided about the congruence of angles and sides between the two triangles.
We have:
- ∠X ≅ ∠L
- ∠P ≅ ∠M
- ∠A ≅ ∠K
- PA ≅ MK
- AX ≅ KL
- XP ≅ LM
From this information, we can analyze each option to see if the corresponding angles and sides match.
Option Analysis:
A. △XPA ≅ △KLM
- Corresponding angles:
- ∠X corresponds to ∠K (not equal)
- ∠P corresponds to ∠L (not equal)
- ∠A corresponds to ∠M (not equal)
- This does not satisfy the criteria for congruence.
B. △PAX ≅ △MKL
- Corresponding angles:
- ∠P corresponds to ∠M (yes)
- ∠A corresponds to ∠K (yes)
- ∠X corresponds to ∠L (yes)
- Corresponding sides:
- PA ≅ MK (yes)
- AX ≅ KL (yes)
- XP ≅ LM (yes)
- This forms a correct congruence statement.
C. △XPA ≅ △MKL
- Corresponding angles:
- ∠X corresponds to ∠M (not equal)
- ∠P corresponds to ∠K (not equal)
- ∠A corresponds to ∠L (not equal)
- This does not satisfy the criteria for congruence.
D. △PAX ≅ △KLM
- Corresponding angles:
- ∠P corresponds to ∠K (not equal)
- ∠A corresponds to ∠M (not equal)
- ∠X corresponds to ∠L (yes)
- This does not satisfy the criteria for congruence.
Conclusion:
The only option that correctly represents the congruence of the triangles based on the given information is B. △PAX≅△MKL.