Question

Can the three segments below form a triangle? Explain how you will change the length of one or two of these segments to form each kind of triangle. If no changes needed enter the original length or state that no changes needed. scalene triangleAB=… BC=…. AC=… equilateral triangleAB = … BC = … AC = …isosceles triangleAB = … BC = … AC = …

Answer 1

ANSWERS

• They cannot form a triangle

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• Scalene triangle: ,AB = 7

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• Equilateral triangle: ,BC = 5, AC = 5

,

• Isosceles triangle: ,AB = 8

Step-by-step explanation

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side,

`\begin{gathered} 14+8>5\Rightarrow true \\ 14+5>8\Rightarrow true \\ 5+8>14\Rightarrow false \end{gathered}`

Hence, these side lengths cannot form a triangle.

To form a scalene triangle one of the shortest sides must be larger, for example, AB should be 7, instead of 5. Other combinations are possible as well.

To form an equilateral triangle all sides must have the same length, for example, AB = BC = AC = 5

To form an isosceles triangle, two of the sides must have the same length, while the third side has a different length, for example, AB = 8

To form all three kinds of triangles, the first rule must be valid as well.