A triangle has no congruent size the length of two sides of the triangle are a b and bdd use the number line to determine the length of a b and BD then use the triangle inequality theorem to determine which two segments have length that could be used as the third side of the triangle select a response containing two possible answers
To determine the length of \(a\), \(b\), and \(BD\), we can use the number line.
Let's assume that \(b\) is on the number line at 0, so \(a\) would be at distance \(a\) to the right of \(b\) and \(BD\) would be at distance \(b\) to the right of \(b\).
Now, using the given information, we know that the lengths from \(a\) to \(b\) and from \(b\) to \(d\) are \(a\) and \(bd\) respectively.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, the possible pairs that could make the third side of the triangle are:
1. \(a + b > bd\) and \(b + bd > a\)
2. \(a + bd > b\) and \(b + a > bd\)
So, the two possible answers are:
1. \(a + b > bd\) and \(b + bd > a\)
2. \(a + bd > b\) and \(b + a > bd\)