Question
Name the pair of congruent triangles, and state how you can prove they are congruent.
Given: CZ = WX
answers:
XWC and CZX, SAS
CZX and XWC, SSS
XCZ and CXW, SAS
WCX and ZCX, SSS
Given: CZ = WX
answers:
XWC and CZX, SAS
CZX and XWC, SSS
XCZ and CXW, SAS
WCX and ZCX, SSS
Answers
GPT-4o mini
To determine the pair of congruent triangles and how to prove them congruent based on the given information \(CZ = WX\), we can analyze the answers provided.
Given that \(CZ = WX\) suggests that one side of triangle CZX is congruent to one side of triangle XWC. To assess which triangles are congruent:
1. **Identify the triangles in the answer choices:**
- **Choice 1:** XWC and CZX, SAS
- **Choice 2:** CZX and XWC, SSS
- **Choice 3:** XCZ and CXW, SAS
- **Choice 4:** WCX and ZCX, SSS
2. **Check which pairs of triangles are relevant to the given side lengths.**
Here, note that if \(CZ = WX\), then triangles XWC and CZX must be relevant.
3. **Evaluate the congruence conditions:**
- For **SAS (Side-Angle-Side)**: We need to show that two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.
- For **SSS (Side-Side-Side)**: All three corresponding sides must be congruent.
As none of the given options clearly indicate other side or angle relationships, based on only the provided information, you would most likely choose **Choice 1:** XWC and CZX, SAS if there are other congruent sides (which the problem does not clarify).
However, without additional information about angles or the lengths of other sides, it is difficult to definitively conclude without making assumptions.
#### Conclusion:
**XWC and CZX, SAS** would be the best answer given the provided information, assuming that the necessary sides and the included angle are congruent as per SAS criteria.
Given that \(CZ = WX\) suggests that one side of triangle CZX is congruent to one side of triangle XWC. To assess which triangles are congruent:
1. **Identify the triangles in the answer choices:**
- **Choice 1:** XWC and CZX, SAS
- **Choice 2:** CZX and XWC, SSS
- **Choice 3:** XCZ and CXW, SAS
- **Choice 4:** WCX and ZCX, SSS
2. **Check which pairs of triangles are relevant to the given side lengths.**
Here, note that if \(CZ = WX\), then triangles XWC and CZX must be relevant.
3. **Evaluate the congruence conditions:**
- For **SAS (Side-Angle-Side)**: We need to show that two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.
- For **SSS (Side-Side-Side)**: All three corresponding sides must be congruent.
As none of the given options clearly indicate other side or angle relationships, based on only the provided information, you would most likely choose **Choice 1:** XWC and CZX, SAS if there are other congruent sides (which the problem does not clarify).
However, without additional information about angles or the lengths of other sides, it is difficult to definitively conclude without making assumptions.
#### Conclusion:
**XWC and CZX, SAS** would be the best answer given the provided information, assuming that the necessary sides and the included angle are congruent as per SAS criteria.