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Part III: Change the length of one or two segments in Part II to form each kind of triangle. (3 points, 1 point each)

a. Scalene triangle
[tex]\[ AB = \quad BC = \quad AC = \][/tex]

b. Equilateral triangle
[tex]\[ AB = \quad BC = \quad AC = \][/tex]

c. Isosceles triangle
[tex]\[ AB = \quad BC = \quad AC = \][/tex]



Answer :

GinnyAnswer
Sure, let's discuss the changes in segment lengths needed to form different types of triangles. For each triangle type, I will specify the lengths of [tex]\( AB \)[/tex], [tex]\( BC \)[/tex], and [tex]\( AC \)[/tex].

### a. Scalene Triangle
A scalene triangle is a triangle in which all three sides have different lengths. For this type of triangle:
- [tex]\( AB = 5 \)[/tex]
- [tex]\( BC = 7 \)[/tex]
- [tex]\( AC = 10 \)[/tex]

### b. Equilateral Triangle
An equilateral triangle is a triangle in which all three sides are of equal length. For this type of triangle:
- [tex]\( AB = 6 \)[/tex]
- [tex]\( BC = 6 \)[/tex]
- [tex]\( AC = 6 \)[/tex]

### c. Isosceles Triangle
An isosceles triangle is a triangle in which at least two sides are of equal length. For this type of triangle:
- [tex]\( AB = 5 \)[/tex]
- [tex]\( BC = 5 \)[/tex]
- [tex]\( AC = 8 \)[/tex]

Therefore, the lengths of segments [tex]\( AB \)[/tex], [tex]\( BC \)[/tex], and [tex]\( AC \)[/tex] to form each type of triangle are as follows:

#### Scalene Triangle (all sides different)
- [tex]\( AB = 5 \)[/tex]
- [tex]\( BC = 7 \)[/tex]
- [tex]\( AC = 10 \)[/tex]

#### Equilateral Triangle (all sides equal)
- [tex]\( AB = 6 \)[/tex]
- [tex]\( BC = 6 \)[/tex]
- [tex]\( AC = 6 \)[/tex]

#### Isosceles Triangle (two sides equal)
- [tex]\( AB = 5 \)[/tex]
- [tex]\( BC = 5 \)[/tex]
- [tex]\( AC = 8 \)[/tex]

These are the necessary segment lengths to form the required types of triangles.

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