If X is congruent with L, P is congruent with M, A is congruent with K, PA is congruent with Mk, and AX is congruent with KL and XP is congruent with LM which option correct congruence statement
1:PAX is congruent KLM
2:PAX is congruent with MKl
3: XPA is congruent with MKL
4:XPA is congruent with KLM
The correct congruence statement is:
4: XPA is congruent with KLM
Based on the given information, the correct congruence statement is:
4: XPA is congruent with KLM
To determine the correct congruence statement, we need to understand the properties of congruence. In geometry, two triangles are congruent if they have the same size and shape. This means that their corresponding sides and angles are equal.
Given the information provided:
- X is congruent to L
- P is congruent to M
- A is congruent to K
- PA is congruent to Mk
- AX is congruent to KL
- XP is congruent to LM
Let's analyze the given options:
1: PAX is congruent to KLM
We cannot directly conclude this statement from the given information because it involves the angles PAX and KLM, which are not specifically mentioned.
2: PAX is congruent to MKl
The given information does not mention anything about the sides or angles (Kl) relating to this option. Therefore, this option is not correct.
3: XPA is congruent to MKL
This statement involves the angles XPA and MKL, which are not specifically mentioned in the given information. Therefore, this option is not correct.
4: XPA is congruent to KLM
This statement involves the sides and angles that are mentioned in the given information:
- AX is congruent to KL
- PA is congruent to Mk
- XP is congruent to LM
Since all three pairs of corresponding sides and angles are equal, we can conclude that XPA is congruent to KLM. Therefore, option 4 is the correct congruence statement.
Answer: 4: XPA is congruent to KLM