Question
Triangles S T U and W V X are congruent. Angles W and W are congruent, T and V are congruent, and U and X are congruent.
Which of the following statements are correct based on the diagram? Select all that apply.
Segment U T is congruent to segment X V
Angle S is congruent to angle V
Segment S T is congruent to segment W V
Angle V is congruent to angle T
Segment U S is congruent to segment X V
Which of the following statements are correct based on the diagram? Select all that apply.
Segment U T is congruent to segment X V
Angle S is congruent to angle V
Segment S T is congruent to segment W V
Angle V is congruent to angle T
Segment U S is congruent to segment X V
Answers
GPT-4o mini
Given that triangles STU and WVX are congruent, we can conclude the following based on the properties of congruent triangles:
1. **Segment UT is congruent to segment XV** - This is not necessarily correct; we have no direct evidence from the congruence of triangles STU and WVX that segments UT and XV are congruent since U and X are not vertices in the congruence condition provided.
2. **Angle S is congruent to angle V** - This statement is not correct since angles S and V correspond to different triangles (S is from triangle STU, and V is from triangle WVX).
3. **Segment ST is congruent to segment WV** - This is a true statement based on the congruence of triangles; corresponding sides of congruent triangles are congruent.
4. **Angle V is congruent to angle T** - This statement is correct because they are corresponding angles within the congruent triangles.
5. **Segment US is congruent to segment XV** - This statement is also not correct since US and XV come from different triangles and are not given to be the corresponding parts.
Therefore, based on the properties of congruent triangles, the correct statements are:
- Segment ST is congruent to segment WV.
- Angle V is congruent to angle T.
1. **Segment UT is congruent to segment XV** - This is not necessarily correct; we have no direct evidence from the congruence of triangles STU and WVX that segments UT and XV are congruent since U and X are not vertices in the congruence condition provided.
2. **Angle S is congruent to angle V** - This statement is not correct since angles S and V correspond to different triangles (S is from triangle STU, and V is from triangle WVX).
3. **Segment ST is congruent to segment WV** - This is a true statement based on the congruence of triangles; corresponding sides of congruent triangles are congruent.
4. **Angle V is congruent to angle T** - This statement is correct because they are corresponding angles within the congruent triangles.
5. **Segment US is congruent to segment XV** - This statement is also not correct since US and XV come from different triangles and are not given to be the corresponding parts.
Therefore, based on the properties of congruent triangles, the correct statements are:
- Segment ST is congruent to segment WV.
- Angle V is congruent to angle T.