Use the image to answer the 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. (1 point) Responses CD and AC cap c cap d and cap A cap c BC and AD cap b cap c and cap A cap d BC and CD cap b cap c and cap c cap d AC and BC

Question

Use the image to answer the 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. (1 point) Responses CD and AC cap c cap d and cap A cap c BC and AD cap b cap c and cap A cap d BC and CD cap b cap c and cap c cap d AC and BC

Answer 1

Based on the number line, we can determine that AB has a length of 5 units, while BD has a length of 3 units.

Now, let's apply the Triangle Inequality Theorem. According to the theorem, for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.

Using this, we can determine that the possible combinations of two segments that could be used as the third side of the triangle are:

1. CD and AC or cap c and cap d
2. BC and AD or cap b and cap c