Question

Investigate the construction of a triangle in these portfolio activities. Use what you have learned about the Triangle Angle Sum Theorem and the Triangle Inequality Theorem to create your submissions. Record your answers below.
Question 1
Find three objects (sticks utensils yarn, etc.)that could represent the sides of a Triangle. Can you make a triangle with these three objects? Use the Triangle Inequality Theorem explain why or why not.
Write answer below.
Measurements of each object

Answer 1

To investigate the construction of a triangle using three objects, we first need to choose three objects that could represent the sides of a triangle and measure their lengths. Let's take the following examples:

1. **Object A**: A stick measuring 5 cm
2. **Object B**: A stick measuring 7 cm
3. **Object C**: A stick measuring 9 cm

### Triangle Inequality Theorem

The Triangle Inequality Theorem states that for any three lengths \(a\), \(b\), and \(c\) to form a triangle, the following conditions must be met:
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

### Measurements
- **Object A (5 cm)**
- **Object B (7 cm)**
- **Object C (9 cm)**

### Applying the Triangle Inequality Theorem

Let’s check if these measurements can form a triangle by applying the theorem:

1. **Check \(5 + 7 > 9\)**:
- \(12 > 9\) (True)

2. **Check \(5 + 9 > 7\)**:
- \(14 > 7\) (True)

3. **Check \(7 + 9 > 5\)**:
- \(16 > 5\) (True)

### Conclusion
Since all three conditions of the Triangle Inequality Theorem are satisfied, we can conclude that it is possible to form a triangle with the three objects (5 cm, 7 cm, and 9 cm).

Thus, using these measurements, we can successfully construct a triangle.