Question

Use the conditional: If $\overline{AB}$and $\overline{CD}$intersect, then $\overrightarrow{AB}$and $\overrightarrow{CD}$intersect.

Rewrite the following pair of conditionals as a biconditional:

$\overline{AB}\cong \overline{CD}$if $AB=CD$; $\overline{AB}\cong \overline{CD}$only if $AB=CD$.

Short answer

The answer for the provided statement is $\overline{AB}\cong \overline{CD}$if and only if $AB=CD$.

Step-by-step solution

Step 1. Observe the given symbols.

The symbols represent the condition that is for two segments that $\overline{AB}\cong \overline{CD}$when $AB=CD$.

Step 2. Identify the biconditional.

Biconditional of the provided conditional will be the regeneration of it with a set of words which are “if and only if” so write the biconditional that is: $\overline{AB}\cong \overline{CD}$if and only if $AB=CD$.

Step 3. State whether the biconditional is true or not.

There is no difference between the original conditional and the biconditional so the biconditional is true.