Question

Which set of measuring create many triangles

15cm,3cm,18cm
10cm,10cm,10cm
65degree,5degree,110 degree
91degree,54degree,34degree

Answer 1

Which can make many triangles

Answer 2

To determine which set of measurements can create triangles, we can apply the properties of triangles.

1. **Three Side Lengths (15 cm, 3 cm, 18 cm)**:
We can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
- 15 + 3 > 18 (False)
- 15 + 18 > 3 (True)
- 3 + 18 > 15 (True)

Since 15 + 3 is not greater than 18, this set cannot form a triangle.

2. **Three Side Lengths (10 cm, 10 cm, 10 cm)**:
This is an equilateral triangle.
- 10 + 10 > 10 (True)
- 10 + 10 > 10 (True)
- 10 + 10 > 10 (True)

This set can form a triangle.

3. **Three Angles (65 degrees, 5 degrees, 110 degrees)**:
The sum of the angles in a triangle must equal 180 degrees.
- 65 + 5 + 110 = 180 (True)

This set can form a triangle.

4. **Three Angles (91 degrees, 54 degrees, 34 degrees)**:
Again, check the sum of the angles.
- 91 + 54 + 34 = 179 (False)

This set cannot form a triangle since the angles do not sum to 180 degrees.

### Conclusion:
The sets that can create triangles are:
- **10 cm, 10 cm, 10 cm** (equilateral triangle)
- **65 degrees, 5 degrees, 110 degrees**

The other sets **(15 cm, 3 cm, 18 cm)** and **(91 degrees, 54 degrees, 34 degrees)** cannot form triangles.