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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
b. Equilateral triangle
c. Isosceles triangle

[tex]\[ AB = \][/tex]
[tex]\[ AB = \][/tex]
[tex]\[ AB = \][/tex]

[tex]\[ BC = \][/tex]
[tex]\[ BC = \][/tex]
[tex]\[ BC = \][/tex]

[tex]\[ AC = \][/tex]
[tex]\[ AC = \][/tex]
[tex]\[ AC = \][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's determine the side lengths for each type of triangle:

a. Scalene Triangle: A scalene triangle has all sides of different lengths.

To form a scalene triangle:
- [tex]\( AB = 3 \)[/tex]
- [tex]\( BC = 4 \)[/tex]
- [tex]\( AC = 5 \)[/tex]

In this case, all three sides are of different lengths, thus forming a scalene triangle.

b. Equilateral Triangle: An equilateral triangle has all sides of equal lengths.

To form an equilateral triangle:
- [tex]\( AB = 6 \)[/tex]
- [tex]\( BC = 6 \)[/tex]
- [tex]\( AC = 6 \)[/tex]

Each side is equal, satisfying the condition for an equilateral triangle.

c. Isosceles Triangle: An isosceles triangle has two sides of equal length and the third side of a different length.

To form an isosceles triangle:
- [tex]\( AB = 7 \)[/tex]
- [tex]\( BC = 7 \)[/tex]
- [tex]\( AC = 5 \)[/tex]

Here, two sides ([tex]\( AB \)[/tex] and [tex]\( BC \)[/tex]) are of equal length, and the third side ([tex]\( AC \)[/tex]) is different, forming an isosceles triangle.

In conclusion, the lengths for each type of triangle are:
- For the scalene triangle: [tex]\( AB = 3 \)[/tex], [tex]\( BC = 4 \)[/tex], [tex]\( AC = 5 \)[/tex]
- For the equilateral triangle: [tex]\( AB = 6 \)[/tex], [tex]\( BC = 6 \)[/tex], [tex]\( AC = 6 \)[/tex]
- For the isosceles triangle: [tex]\( AB = 7 \)[/tex], [tex]\( BC = 7 \)[/tex], [tex]\( AC = 5 \)[/tex]

These values ensure that each triangle fits its respective classification.
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