Question

ab and ac are opposite rays. all of the following are true except ______ a. a, b, c are coplanar b. a, b, c are collinear c. a is between b and c d. ab = ac

Explanation:

Answer:

To determine the false statement when \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\) are opposite rays:

• Opposite rays lie on the same line (collinear) and share the same endpoint, so they are coplanar (lie in the same plane) and \(A\), \(B\), \(C\) are collinear with \(A\) between \(B\) and \(C\).
• However, \(AB = AC\) is not necessarily true. Opposite rays only require \(A\) to be the common endpoint and \(B\), \(C\) to be on a straight line in opposite directions, not that the lengths \(AB\) and \(AC\) are equal.

So the false statement is \(\boldsymbol{AB = AC}\) (the last option).