Given that BD �Û AC, which of the following statements is NOT necessarily true?
To determine which statement is NOT necessarily true, we need to consider the given information and analyze each statement individually.
The given information is: BD ≠ AC, which means that BD is not equal to AC.
Now let's evaluate each statement:
Statement 1: BD < AC - This statement is necessarily true since the given information does not provide any restrictions on the relative lengths of BD and AC. Therefore, it is possible for BD to be less than AC.
Statement 2: BD > AC - This statement is necessarily false. Since BD is not equal to AC, it is not possible for BD to be greater than AC.
Statement 3: AC < BD - This statement is necessarily true. Since BD is not equal to AC, it is possible for BD to be larger than AC.
Statement 4: AC > BD - This statement is necessarily false. Since BD is not equal to AC, it is not possible for AC to be greater than BD.
Based on the analysis, the statement that is NOT necessarily true is Statement 4: AC > BD.