A triangle has no congruent sides. The lengths of two sides of the triangle are AB and BD use the number line above to determine the lengths of AB and BD then use the triangle inequality theorem to determine which two segments have lengths that could be used as the third side of the triangle select a response containing 2 possible answers

Question

A triangle has no congruent sides. The lengths of two sides of the triangle are AB and BD use the number line above to determine the lengths of AB and BD then use the triangle inequality theorem to determine which two segments have lengths that could be used as the third side of the triangle select a response containing 2 possible answers

Answer 1

With the information given on the number line, we can determine that the lengths of AB and BD are 4 and 5, respectively.

Using 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 lengths for the third side of the triangle are:
1) AC = 6
2) CD = 1