If ∠X≅∠L , ∠P≅∠M , ∠A≅∠K , PA¯¯¯¯¯¯¯¯≅∠MK¯¯¯¯¯¯¯¯¯¯ , AX¯¯¯¯¯¯¯¯≅∠KL¯¯¯¯¯¯¯¯ , and XP¯¯¯¯¯¯¯¯≅∠LM¯¯¯¯¯¯¯¯¯ , which option below shows a correct congruence statement?(1 point)
△XPA≅△MKL
△XPA≅△KLM
△PAX≅△MKL
△PAX≅△KLM
△PAX≅△KLM
The correct congruence statement would be:
△PAX≅△KLM
To determine the correct congruence statement, we need to analyze the given information and apply the corresponding congruence criteria.
From the given information, we know that:
1. ∠X ≅ ∠L (Angle X is congruent to Angle L)
2. ∠P ≅ ∠M (Angle P is congruent to Angle M)
3. ∠A ≅ ∠K (Angle A is congruent to Angle K)
4. PA ≅ MK (Segment PA is congruent to segment MK)
5. AX ≅ KL (Segment AX is congruent to segment KL)
6. XP ≅ LM (Segment XP is congruent to segment LM)
Based on the given information, we can conclude that triangles △PAX and △KLM are congruent. This is because we have:
- ∠X ≅ ∠L (corresponding congruent angles)
- ∠P ≅ ∠M (corresponding congruent angles)
- ∠A ≅ ∠K (corresponding congruent angles)
- PA ≅ MK (corresponding congruent sides)
- AX ≅ KL (corresponding congruent sides)
- XP ≅ LM (corresponding congruent sides)
Therefore, the correct congruence statement would be:
△PAX ≅ △KLM