To determine the relationship between the triangles [tex]\( \triangle AQRS \)[/tex] and [tex]\( \triangle ATUV \)[/tex] based on the provided descriptions, we need to analyze the measurements and see if they match certain criteria for congruency and similarity.
### Congruent Triangles
For two triangles to be congruent:
- All corresponding sides must be equal in length.
- All corresponding angles must be equal.
### Similar Triangles
For two triangles to be similar:
- All corresponding angles must be equal.
- The corresponding side lengths must be proportional.
### Analyzing the Descriptions
The given descriptions contain the following measurements:
[tex]\[ 72, 90, 24, 30, 56, 41, 36, 56, 108 \][/tex]
We are to check the relationships using these measurements and determine if they imply congruence or similarity.
#### Verification
1. Congruence Check:
- Congruent triangles must have all corresponding angles and sides equal.
- Since there are no measurements that exactly repeat in a way that all corresponding sides and angles are equal, the triangles are not congruent.
2. Similarity Check:
- Similar triangles must have corresponding angles equal and side lengths proportional.
- Given the descriptions, it's evident that there is no exact proportional relationship among the corresponding sides based on the measurements.
### Conclusion
Based on our analysis:
1. The triangles [tex]\( \triangle AQRS \)[/tex] and [tex]\( \triangle ATUV \)[/tex] are not congruent.
2. The triangles [tex]\( \triangle AQRS \)[/tex] and [tex]\( \triangle ATUV \)[/tex] are not similar.
Thus, none of the given descriptions (A. Congruent, B. Same size, C. Similar, D. Same shape) apply to the relationship between the two triangles. Therefore, the accurate descriptions from the list that apply are:
[tex]\[ \textcolor{blue}{[]} \][/tex]
