Question

Congruency of Triangles Quick Check 1 of 51 of 5 Items 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 △PAX≅△KLM triangle upper P upper A upper X 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 Skip to navigation page 9 of 9 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the correct congruence statement between triangles based on the information provided, we can use the congruency of angles and sides.

We have:
- ∠X ≅ ∠L
- ∠P ≅ ∠M
- ∠A ≅ ∠K
- PA ≅ MK
- AX ≅ KL
- XP ≅ LM

From this information, we can see that:

1. All corresponding angles of triangles XPA and KLM are congruent:
- ∠X ≅ ∠L
- ∠P ≅ ∠M
- ∠A ≅ ∠K

2. All corresponding sides of triangles XPA and KLM are congruent:
- PA ≅ MK
- AX ≅ KL
- XP ≅ LM

Therefore, we can conclude that triangle XPA is congruent to triangle KLM.

The correct congruence statement is:
**△XPA ≅ △KLM**

So the answer is the first option.