Question

The segments shown below could form a triangle.AС4910B15АA. TrueB. False

Answer 1

Given:

`\begin{gathered} AC=9 \\ BC=4 \\ AB=15 \end{gathered}`

To know if the line segments could form a triangle, we use the triangle inequality theorem.

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.

Hence, using the sides given;

`\begin{gathered} 9+4<15 \\ 13<15\ldots\ldots\ldots\ldots\text{.(does not satisfy the triangle inequality theorem)} \\ \\ \text{Also,} \\ 9+15>4 \\ 24>4\ldots\ldots\ldots\ldots(\text{satisfies the triangle inequality theorem)} \\ \\ \text{Lastly,} \\ 4+15>9 \\ 19>9\ldots\ldots\ldots\ldots(\text{satisfies the triangle inequality theorem)} \end{gathered}`

Since 9 + 4 < 15 does not satisfy the triangle inequality theorem, the sum of the two sides is not greater than the third side, then the sides could not be used to form a triangle.

Therefore, the answer is false.