Question
Question 7 of 10 True or false? If two triangles are congruent, then they can be moved so that they line up perfectly. A. True B. False
Ask by Salinas Coles. in the United States
Mar 07,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A. True
Solution
```markdown
### Step-by-Step Explanation
1. **Definition of Congruent Triangles:**
Two triangles are congruent if they have the same size and shape. This means that every corresponding side and angle of the triangles are equal.
2. **Concept of Rigid Motions (Isometries):**
If two figures are congruent, one can be transformed into the other by a series of rigid motions. Rigid motions include:
- **Translation:** Shifting the triangle without rotating it.
- **Rotation:** Rotating the triangle about a point.
- **Reflection:** Flipping the triangle over a line.
3. **Lining Up Perfectly:**
Since congruent triangles have the same size and shape, applying the appropriate combination of rigid motions will make every side and angle match perfectly. This means that one triangle can be repositioned to coincide exactly with the other.
4. **Conclusion:**
Based on the properties of congruent triangles and rigid motions, it is true that if two triangles are congruent, then they can be moved so that they line up perfectly.
Thus, the correct answer is:
**A. True**
```
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A. True! Congruent triangles mean they have the same shape and size, which makes it possible to align them perfectly by moving them around through translation, rotation, or reflection. Imagine two identical puzzle pieces—when you twist and turn them just right, they'll click into place! Now, think about real-world structures like bridges or buildings. Engineers rely on congruence when designing elements to ensure that they fit together perfectly, ensuring strength and stability. It’s the secret behind those neat, symmetrical designs we see all around us!
