To determine the correct congruence statement based on the given information, we can use the Angle-Side-Angle (ASA) congruence criterion or the Side-Angle-Side (SAS) criterion.
We have the following congruencies:
- ∠X ≅ ∠L
- ∠P ≅ ∠M
- ∠A ≅ ∠K
- PA ≅ MK
- AX ≅ KL
- XP ≅ LM
From these congruences, we can observe that:
- The angles ∠X and ∠L correspond to vertices X and K.
- The angles ∠P and ∠M correspond to vertices P and M.
- The angles ∠A and ∠K correspond to vertices A and K.
Using the information available, we can match the triangles by their corresponding angles and sides:
-
In the triangle △XPA:
- ∠X ≅ ∠L
- ∠P ≅ ∠M
- Side PA ≅ Side MK
-
In the triangle △MKL:
- ∠K ≅ ∠A
- Side KL ≅ Side AX
Looking at the congruence statements provided:
- a. △XPA ≅ △MKL
- b. △PAX ≅ △MKL
- c. △PAX ≅ △KLM
- d. △XPA ≅ △KLM
We can conclude that the correct congruence statement based on the information provided is:
a. △XPA ≅ △MKL
This is because all corresponding angles and sides match according to the criteria for triangle congruence.