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≅△KLM
triangle upper X upper P upper A congruent to triangle upper K upper L upper M

△XPA≅△MKL
triangle upper X upper P upper A congruent to triangle upper M upper K upper L

△PAX≅△MKL
triangle upper P upper A upper X congruent to triangle upper M upper K upper L

△PAX≅△KLM
triangle upper P upper A upper X congruent to triangle upper K upper L upper M

Answer 1

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**