Question

Nathan drew a right triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3). AC is the longest side in ΔABC. What must be true for this triangle?

Answer 1

For making this statement true we have to check Triangle Inequality theorem.

Explanation:

Given that,

Triangle ΔABC having three vertices are A (
`x_(1) ,y_(1)`), B(
`x_(2) ,y_(2)`), C (
`x_(3) ,y_(3)`) and AC is the longest side.

from the question,

Diagram of the given scenario is shown below,

According to Triangle Inequality theorem states that sum of any 2 sides of a triangle is always greater than third side.

Taking the ΔABC we have,

`AB + BC > AC`

`AB + AC > BC`

`BC+AC > AB`

This condition must be satisfied for drawing a triangle if any two side sum is lesser than third side it will not form a triangle.

Hence,

For making this statement true we have to check Triangle Inequality theorem.